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Test3 Confidence Interval And Hypothesis Testing

76 Questions
Test3 Confidence Interval And Hypothesis Testing

Sample exam for testing knowledge of Confidence Interval, Hypothesis Testing.

Questions and Answers
  • 1. 
    When is a statistical procedure robust?
    • A. 

      When sample is at least 20% of the population?

    • B. 

      When it is used even though the sample is not SRS.

    • C. 

      When confidence level or the P-value does not change very much even when the conditions are not fully met.

    • D. 

      When the correlation between the test statistic and the P-value is close to 1.0 (or the correlation between the level of confidence and z* ic close to 1.).

  • 2. 
    In order to compare free-throw shooting skills of Deacons versus Teachers, 12 Deacons and 16 Teachers were randomly selected to test the hypotheses: Ho: μDT versus Ha: μDT .  The results of the free-throw shooting skills test are: Two Sample T-test results (without pooled variances): μD=mean of Deacons μT=mean of Teachers Ho: μDT = 0 Ha: μDT < 0
    Difference Sample Mean Std. Err. DF t-stat P-value
    μDT -7.31 4.2917 11 -1.5 0.081
    On the basis of the P-value, what should we conclude at α=0.10?
    • A. 

      The mean free-throw score for Teachers equals the mean for Deacons.

    • B. 

      The mean free-throw score for Teachers is significantly less than the mean for Deacons.

    • C. 

      The mean free-throw score for Deacons is significantly less than the mean for Teachers.

    • D. 

      The mean free-throw score for Deacons is not significantly less than the mean for Teachers.

  • 3. 
    Consider an SRS of size 20 from a Normally distributed population, If x-bar=45 and s=15, what is the appropriate formula for a 95% confidence interval for µ?
    • A. 

      X ̅ ± z*σ / √n

    • B. 

      X ̅ ± t*σ ⁄ √n

    • C. 

      x ̅ ± z*s ⁄ √n

    • D. 

      X ̅± t*s ⁄ √n

  • 4. 
    Consider an SRS of size 16 from a Normally distributed population with σ=16, If x-bar 12x">=45 and s=12, what is the appropriate formula for a 95% confidence interval for µ?
    • A. 

      x ̅ ± z* σ ⁄ √n

    • B. 

      X ̅ ± z* s ⁄ √n

    • C. 

      x ̅ ± t* σ ⁄ √n

    • D. 

      x ̅ ± t* s ⁄ √n

  • 5. 
    You want to compare the daily items sold for two game consoles: Playstation3(PS3) and NintendoWII(WII). Over the next 80 days, 40 days are randomly assigned to PS3 and 40 days to WII. At the end, you compute a 95% confidence interval for the difference in mean daily items sold for the two game consoles to be (-20, 10). On the basis of this confidence interval, can you conclude that there is a significant difference between the mean daily items sold for the two game consoles at α=0.05? (i.e., can you reject  
    • A. 

      No because the mean daily items sold cannot be negative.

    • B. 

      No, because the interval tells us the mean daily items sold for the two game consoles and doesn’t provide information for comparing them.

    • C. 

      No, because the confidence interval contains zero.

    • D. 

      Yes, because the confidence interval contains zero.

    • E. 

      Yes, because we are 95% confident that the difference between the mean daily items sold for PS3 and WII is somewhere between -20 and 10.

  • 6. 
    You want to compare the daily items sold for two game consoles: Playstation3(PS3) and NintendoWII(WII). Over the next 80 days, 40 days are randomly assigned to PS3 and 40 days to WII. At the end, you compute a 95% confidence interval for the difference in mean daily items sold for the two game consoles to be (-20, -10). On the basis of this confidence interval, can you conclude that there is a significant difference between the mean daily items sold for the two game consoles at α=0.05? (i.e., can you reject  
    • A. 

      No because the mean daily items sold cannot be negative.

    • B. 

      No, because the interval tells us the mean daily items sold for the two game consoles and doesn’t provide information for comparing them.

    • C. 

      No, because the confidence interval contains zero.

    • D. 

      Yes, because the confidence interval does not contains zero.

    • E. 

      Yes, because we are 95% confident that the difference between the mean daily items sold for PS3 and WII is somewhere between -20 and 10.

  • 7. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05,  x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of Type II error?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 8. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05,  x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of Type I error?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 9. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of the power of the test?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 10. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70 is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of Type II error?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 11. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of Type I error?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 12. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of the power of the test?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 13. 
           We wish to compare two game consoles on the market which were deemed preferred by video game players. Initial testing leads us to believe that Nintendo WII will be more preferred by video game players than Playstation 3. Eighty players are randomly assigned to the two game consoles so that 40 players get WII and 40 players get PS3. The researcher determines in each case whether or not the game console is preferred by video game players. Which statistical procedure should the researcher use for an appropriate test of significance?
    • A. 

      A one sample t-test for means (not matched pairs).

    • B. 

      A two sample t-test for means.

    • C. 

      A matched pairs t-test for means.

    • D. 

      Analysis of Variance (ANOVA)

    • E. 

      A one sample t confidence interval estimate

  • 14. 
      Researchers want to compare the mean levels of the good cholesterol and in order to do this, they should perform
    • A. 

      A one sample t-test for means (not matched pairs).

    • B. 

      A two sample t-test for means.

    • C. 

      A matched pairs t-test for means.

    • D. 

      Analysis of Variance (ANOVA)

    • E. 

      A one sample t confidence interval estimate

  • 15. 
          A random sample of 70 measurements of the free-throw percentage of Jr. Jazz players gave a mean of .60 and  standard deviation of .10. Which statistical procedure should be used if we want to estimate the true mean free-throw percentage of the JR Jazz players with 95% confidence?
    • A. 

      A one sample t-test for means (not matched pairs).

    • B. 

      A two sample t-test for means.

    • C. 

      A matched pairs t-test for means.

    • D. 

      Analysis of Variance (ANOVA)

    • E. 

      A one sample t confidence interval estimate

  • 16. 
          Students were randomly assigned to each of the three Stats221 classes at BYU Salt Lake Center.  Their final scores after the semester were recorded.  To see if there are differences between the average Final scores among the three classes, what statistical procedure should be used for the data in this study?
    • A. 

      A one sample t-test for means (not matched pairs).

    • B. 

      A two sample t-test for means.

    • C. 

      A matched pairs t-test for means.

    • D. 

      Analysis of Variance (ANOVA)

    • E. 

      A one sample t confidence interval estimate

  • 17. 
          Mangosteen is a fruit containing chemicals called xanthones that are believed to help the body’s cells to function correctly and optimally. In one study four groups of people were compared; the first group was a control group and the other three groups of people were fed either a low dose, a medium dose or a high dose of xanthones from mangosteen. The number of good cells were counted. The following gives the Analysis of Variance (ANOVA) of these data. What can you conclude about the means of the four groups at α=0.05? Assume that the conditions are met for performing this analysis.
    • A. 

      There is no significance difference between the mean count of good cells of the four groups.

    • B. 

      The mean count of good cells is significantly different for all four groups.

    • C. 

      The mean count of good cells of the high dosage group is significantly greater than the mean count of good cells of the control and low dosage.

    • D. 

      On the basis of the P-value, the mean of at least one group differs significantly from the others, but there is no information in the ANOVA outout to determine which mean differs.

  • 18. 
    Mangosteen is a fruit containing chemicals called xanthones that are believed to help the body’s cells to function correctly and optimally. In one study four groups of people were compared; the first group was a control group and the other three groups of people were fed either a low dose, a medium dose or a high dose of xanthones from mangosteen. The number of good cells were counted. The table below gives the Analysis of Variance (ANOVA) of these data.One of the requirements for Analysis of Variances must be equal. On the basis of the output given below, why is that requirement met?Assume that the conditions are met for performing this analysis.
    • A. 

      The P-value for the F test statistic is less than α=0.05.

    • B. 

      The largest standard deviation divided by the smallest standard deviation is less than 2.

    • C. 

      The pooled standard deviation equals 0.4331 which is greater than α=0.05.

    • D. 

      There is no information given in the ANOVA output to determine whether the variances are equal.

  • 19. 
    In practice, if the condition of Normality of the population for t procedures in not met and n < 40, confidence levels and P-values are approximately correct provided:
    • A. 

      α is set very low.

    • B. 

      The sample standard deviation is not large.

    • C. 

      There are no outliers nor strong skewness in the data.

    • D. 

      The data are paired.

  • 20. 
    A study conducted by researchers at BYU investigated the number of months Returned Missionaries get married after coming back from their missions. A random sample of 25 married RM were selected. The average number of months from returning to getting married  for these RM’s was 16 months. When testing Ho: µ = 12 months versus Ha: µ > 12 months, the P-value was found to be 0.04. Which of the following is a correct interpretation of this P-value?
    • A. 

      The probability that the mean number of months from returning to getting married by all RM’s was 112 months is 0.04.

    • B. 

      The probability that the mean number of months from returning to getting married by all RM’s does not exceed 12 months is 0.04.

    • C. 

      Only 4% of the RM’s who get married after 12 months or less after their mission; the 96% of the remaining RM’s get married after more than 12 months of returning from missions.

    • D. 

      If the average number of months RM’s get married after their mission was indeed 12 months, the probability that RM’s get married after 16 months or greater is .04.

  • 21. 
    The Provo Recreational Office conducted a research of the free-throw percentage of Jr Jazz kids. A percentage of 60% is a “basic” shooting ability and a percentage of 90% is “proficient”. Percentages for a random sample of 1500 Jr Jazz kids from Provo had a mean of 55% with a standard deviation of 20%. What is the value of the standard error of the mean?
    • A. 

      0.0136

    • B. 

      0.1876

    • C. 

      0.5164

    • D. 

      1.8754

    • E. 

      4.5164

  • 22. 
    The average hours spent per week doing the Stats221 homework for BYU students has been  10 hours with a standard deviation of 4 hours. The Statistics Department wanted to test the hypotheses Ho: µ=10 versus  Ha: µ<10.  They selected an α=0.05 and took a random sample of 100 students who had taken the class.  The sample average obtained was 9.75 hours.  This result was statistically significant with a P-value <0.01.  Are these results also practically significant?
    • A. 

      No, because a 15-minute difference is probably too small to matter.

    • B. 

      No, because the sample is not large enough.

    • C. 

      Yes, because the P-value is less than α

    • D. 

      Yes, because the observed mean is less than 10.

    • E. 

      Yes, because results that are statistically significant are also practically significant.

  • 23. 
    In order to estimate the mean GPA for BYU students, a researcher takes a SRS of GPAs for 81 students.  A 96% confidence interval for the mean GPA was computed to be (2.84, 3.06) using  x-bar= 2.95 and s=0.5.  On the basis of this confidence interval, can we conclude at alpha= 0.04 that the mean GPA for BYU students differs from 3.1?
    • A. 

      No, because 3.1 is within one standard deviation of the sample mean

    • B. 

      No, because the confidence interval does not include the value 3.1.

    • C. 

      Yes, because the BYU students are smarter.

    • D. 

      Yes, because the sample mean of 2.95 is less than 3.1.

    • E. 

      Yes, because the confidence interval does not include the value 3.1.

  • 24. 
    The life in hours of a particular brand of plasma TV is advertised to have a mean of 30,000 hours. A nationwide electronics chain wants to determine whether to purchase this particular brand. They decide to test a sample of the plasma tvs and purchase these plasma tv unless the test of significance shows evidence that the mean is less 30,000 hours. In other words, they will test the hypotheses ho: µ =30,000 versus Ha: µ < 30,000 and purchase the plasma tv if they fail to reject the null hypotheses. If they reject the null hypothesis, they will not purchase this particular brand of plasma tv. What is the type I error of this test?
    • A. 

      Decide to purchase the plasma tv when the mean life in hours really is 30,000 hours.

    • B. 

      Decide to purchase the plasma tv when the mean life in hours reall is less than 30,000 hours.

    • C. 

      Decide NOT to purchase the plasma tv when the mean life in hours really is 30,000 hours.

    • D. 

      Decide NOT to purchase the plasma tv when the mean life in hours really is less than 30,000 hours.

  • 25. 
    While performing a statistical test of hypotheses, we decide to reject the null hypothesis .What can we say about the Type I and type II errors of our decision?
    • A. 

      We did not make an error because the P-value is small

    • B. 

      We made a type II error, but not a type I error

    • C. 

      We made a type I error, but not a type II error

    • D. 

      We made both a type I and a type II error

  • 26. 
    While performing a statistical test of hypotheses, we decide to fail to reject the null hypothesis. What can we say about the Type I and type II errors of our decision?
    • A. 

      We did not make an error because the P-value is small

    • B. 

      We made a type II error, but not a type I error

    • C. 

      We made a type I error, but not a type II error

    • D. 

      We made both a type I and a type II error

  • 27. 
    An SRS of 500 students in BYU-Provo (population 25,000) responded to a survey which asked their GPA.  A 95% confidence interval for the mean GPA was obtained.  This survey was also given to a separate SRS of 500 students at the BYU-Salt Lake Center (population 7,000) who also answered the GPA question.  A separate 95% confidence interval statement about the mean GPA of all students in the BYU-Slat Lake Center was also constructed.  Assume the standard deviation, s, is known and is the same for both groups.  The margin of error for the BYU-Salt Lake Center is
    • A. 

      The same as in BYU-Provo, because the two sample sizes are the same.

    • B. 

      Smaller than in BYU-Provo, because the population is much larger in BYU-Provo than BYU-Salt Lake Center.

    • C. 

      Larger than BYU-Provo, because there are fewer students in BYU-Salt Lake

    • D. 

      May be either smaller or larger than BYU-Provo.

  • 28. 
    Coach Sloan suspects that the supplier of the basketball uniforms are sending shirts that easily get torn.  He plans to randomly select some shirts from the next batch and perform a test of significance. What can he do to ensure that the power of the test is high?
    • A. 

      Take a small sample of shirts.

    • B. 

      Take a large sample of shirts.

    • C. 

      Wear each one of them.

    • D. 

      Let the other team wear them.

  • 29. 
    A study was conducted to determine the average GPA of students enrolled at the BYU Salt Lake Center.  A random sample of 50 students was selected, the mean GPA computed and a 90% confidence interval obtained.  The resulting confidence interval is (2.35, 3.87).  This interval gives us
    • A. 

      The range of reasonable values for the true mean GPA of students enrolled at the BYU Salt Lake Center.

    • B. 

      The range of reasonable values for the sample mean GPA of students enrolled at the BYU Salt Lake Center.

    • C. 

      The range of reasonable values for the true standard deviation of GPA of students enrolled at the BYU Salt Lake Center.

    • D. 

      The range for 90% of GPA’s of all students enrolled at the BYU Salt Lake Center.

  • 30. 
    Suppose that a researcher  would like to predict the results of mayoral election on 20 cities in Utah.  We randomly poll 1501 voters from all these cities.  For each city he either “called” a winner or declared the election “too close to call.” The researcher correctly predicted the outcome of 19 elections.  However, for one of the mayoral election, the researcher “called Anderson the winner when Sotomayor actually won the election.  What is the most likely explanation for this mistake?
    • A. 

      The researcher is biased against minorities.

    • B. 

      The researcher does not like Sotomayor.

    • C. 

      Multiple analyses increase the chances of making a Type I error.

    • D. 

      Multiple analyses increase the chances of making a Type II error.

  • 31. 
    Which one of the following situations will best allow a cause-and-effect conclusion about the relationship between smoking and lung cancer?
    • A. 

      Take a random sample of 100 mean, ask them who smoke and who does not. Record the incidence of lung cancer between those who smoke and those who do not.

    • B. 

      Ask for volunteer of 100 mean, ask them who smoke and who does not. Record the incidence of lung cancer between those who smoke and those who do not.

    • C. 

      Take a random sample of 100 men. Randomly assign them into two groups. Ask the first group to smoke for 10 years and the other group not to smoke. After 10 years measure the incidence of lung cancer between the two groups using a two sample t-test.

    • D. 

      Randomly ask 100 lawyers whether smoking causes cancer.

  • 32. 
    A study was conducted using growing rats to examine the effect of jumping height on the strength of bones.  Thirty rats were randomly allocated into groups.  The first group of rats did low jumps of 30 cm. And the second group of rats did high jumps of 60 cm.  After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats was measured in mg/cm3.  What is the response variable?
    • A. 

      Growing rats

    • B. 

      Height of jump

    • C. 

      Bone density as measured in mg/cm3.

    • D. 

      Age of rat

  • 33. 
    The following hypotheses were tested:  Ho: µ=75 versus  Ha: µ > 75 where  µ is the true mean score for Stats221 finals. The test scores of a random sample of students who have taken Stats221 had a mean x-bar = 78. The hypothesis test produced a P-value of 0.314. With alpha=0.05, do the data give sufficient evidence that the mean final score is greater than 75?
    • A. 

      No, because the p-value is not less than alpha

    • B. 

      No, because the results are statistical significant.

    • C. 

      No, because the p-value is less than alpha.

    • D. 

      Yes, because the p-value is not less than alpha.

    • E. 

      Yes, because the p-value is less than alpha.

  • 34. 
    The following hypotheses were tested: Ho: µ=75 versus Ha: µ > 75 where  µ is the true mean score for Stats221 finals. The test scores of a random sample of students who have taken Stats221 had a mean x-bar = 78. The hypothesis test produced a P-value of 0.0314. With alpha=0.05, do the data give sufficient evidence that the mean final score is greater than 75?0
    • A. 

      No, because the p-value is not less than alpha

    • B. 

      No, because the results are statistical significant.

    • C. 

      No, because the p-value is less than alpha.

    • D. 

      Yes, because the p-value is not less than alpha.

    • E. 

      Yes, because the p-value is less than alpha.

  • 35. 
    Which one of the following statements best describes the logic of tests of significance?
    • A. 

      An outcome that is quite likely to happen if Ho were true is good evidence that Ho is true.

    • B. 

      If the probability of Ho being true is very small, then Ho cannot be true.

    • C. 

      If the probability of an outcome occurring is quite likely, then the claim as stated in Ho about the outcome must be correct.

    • D. 

      An outcome that would rarely happen if Ho were true is good evidence that Ho is not true.

  • 36. 
    For a one sided test on µ with σ known, the P-value is represented as the area in the tail of a Normal curve. What does this Normal curve represent?
    • A. 

      Values of the measurements in the sample data set.

    • B. 

      All possible measurements for the response variable and their frequencies.

    • C. 

      The population of measurements about which we wish to make an inference.

    • D. 

      All possible values of x-bars and how often they occur if Ho were true.

  • 37. 
    GPA of students of a specified population are Normally distributed with known standard deviation of 1.1 points. A  95% confidence interval, (2.35, 3.87), was calculated from a simple random sample of twenty-five students.  Which of the following is a correct interpretation of “95% confidence”?
    • A. 

      If this study were to be repeated a large number of times, approximately 95% of the confidence interval would include the true mean.

    • B. 

      95% of the students’ GPA in the population are contained in the confidence interval.

    • C. 

      The interval contains 95% of the sample GPAs.

    • D. 

      If this study were to be repeated a large number of times, 95% of the sample means would be included in this particular confidence interval: (2.35, 3.87).

  • 38. 
    The significance level is set at α=.05 and a hypothesis test results in a P-value of .02. Which one of the following is a correct conclusion based on the P-value?
    • A. 

      The data are consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.

    • B. 

      The data are consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • C. 

      The data are not consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.

    • D. 

      The data are not consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • E. 

      There is a 2% chance that the null hypothesis is true. Therefore, we reject the null hypothesis.

  • 39. 
    The significance level is set at α=.01 and a hypothesis test results in a P-value of .02. Which one of the following is a correct conclusion based on the P-value?
    • A. 

      The data are consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.

    • B. 

      The data are consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • C. 

      The data are not consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • D. 

      There is a 2% chance that the null hypothesis is true. Therefore, we reject the null hypothesis.

    • E. 

      There is a 2% chance that the alternative hypothesis is true. Therefore, we accept the null hypothesis.

  • 40. 
    Based on a random sample of 50 students and a known population and sigma, a 90% confidence interval for the mean GPA of all students was calculated as (2.35, 3.87).  Which of the following is a correct statement regarding this confidence interval?
    • A. 

      90% of the GPA of students are between (2.35, 3.87).

    • B. 

      90% of the time, the mean GPA of students will be in the interval from 2.35 to 3.87.

    • C. 

      We are 90% confident that the mean GPA of students is between 2.35 and 3.87.

    • D. 

      We are 90% confident that the interval (2.35, 3.87) contains the mean GPA of this sample of 50 students.

  • 41. 
    In addition to having an SRS, what should be checked in order to validly use the formula when n=15?
    • A. 

      No other checks necessary.

    • B. 

      Whether the plot of the population is approximately Normal.

    • C. 

      No pattern in the residual plot.

    • D. 

      No outliers or strong skewness in a plot of the data.

  • 42. 
    A SRS of 64 BYU students found that the average GPA was x-bar=2.7.  Assuming the  population standard deviation is known to be 0.3, a margin of error for a 95% confidence interval for the population average GPA is calculated to be  0.0735.  Which action below would result in a smaller margin of error?
    • A. 

      Using a confidence level of 99%

    • B. 

      Using a sample of 50 students.

    • C. 

      Using a sample of 100 students.

    • D. 

      Taking a different sample of 64 students.

  • 43. 
    A SRS of 64 BYU students found that the average GPA was x-bar=2.7.  Assuming the  population standard deviation is known to be 0.3, a margin of error for a 95% confidence interval for the population average GPA is calculated to be  0.0735.  Which action below would result in a larger margin of error?
    • A. 

      Using a confidence level of 99%.

    • B. 

      Using a confidence level of 90%

    • C. 

      Using a sample of 100 students

    • D. 

      Taking a different sample of 64 students.

  • 44. 
    Researchers have postulated that because of differences in teachers, students at the BYU Salt Lake Center should have a higher GPA than BYU-Provo students.  Suppose the mean GPA of BYU-Provo students is known to be 3.2.  What hypothesis are being tested?
    • A. 

      Ho: µ = 3.2 and Ha: µ > 3.2

    • B. 

      Ho: µ = 3.2 and Ha: µ < 3.2

    • C. 

      Ho: µ = 3.2 and Ha: µ ≠ 3.2

    • D. 

      Ho: x ̅ =3.2 and Ho: x ̅ >3.2

  • 45. 
    Researchers have postulated that there is no  differences in GPA of the BYU Salt Lake Center and  BYU-Provo students.  Suppose the mean GPA of BYU-Provo students is known to be 3.2.  What hypothesis are being tested?
    • A. 

      Ho: µ = 3.2 and Ha: µ > 3.2

    • B. 

      Ho: µ = 3.2 and Ha: µ < 3.2

    • C. 

      Ho: µ = 3.2 and Ha: µ ≠ 3.2

    • D. 

      Ho: x ̅ =3.2 and Ho: x ̅ ≠ 3.2

  • 46. 
    Which of the following questions does a test of significance answer?
    • A. 

      Is the sample or experiment properly designed?

    • B. 

      Is the observed effect too large to be due to chance alone?

    • C. 

      How much confidence can be placed in the observed effect?

    • D. 

      What is the probability that the parameter is different from the statistic?

  • 47. 
    Suppose we want a 95% confidence interval for the average amount spend on dates at BYU.  The amount spend on dates follow a normal distribution with a standard deviation σ= $20.  How large should the sample be so that 95% confidence interval has a margin of error of $3?
    • A. 

      170

    • B. 

      170.7

    • C. 

      171

    • D. 

      100

  • 48. 
     When performing a one-sample t-test of Ho: µ=µo versus Ha: µ>µo, the observed effect is equal to the difference between x-bar and µo (i.e.,x-bar - µo). For a fixed sample size, if the observed effect were to increase, what would happen to the P-value?
    • A. 

      It would get smaller.

    • B. 

      It would stay the same.

    • C. 

      It would get bigger.

  • 49. 
     When performing a one-sample t-test of Ho: µ=µo versus Ha: µ>µo, the observed effect is equal to the difference between x-bar and µo (i.e.,x-bar - µo). For a fixed sample size, if the observed effect were to decrease, what would happen to the P-value?
    • A. 

      It would get smaller.

    • B. 

      It would stay the same.

    • C. 

      It would get bigger.

  • 50. 
    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ>65% and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 51. 
    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ<65% and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 52. 
    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ ≠ 65%  and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test?
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 53. 
    The P-value for a significance test is defined as
    • A. 

      The probability that the null hypothesis is true.

    • B. 

      The probability that the alternative hypothesis is wrong.

    • C. 

      The probability of rejecting the null hypothesis when in fact the null hypothesis is true.

    • D. 

      The probability that the alternative hypothesis is false, assuming the null hypothesis is true.

    • E. 

      . the probability of obtaining a test statistic that has a value at least as extreme as that actually observed, assuming the null hypothesis is true.

  • 54. 
    Coach Rose claims that by using his method of shooting,  basketball players can increase their scores by an average of 15 points.  Wesley, a  former basketball player is skeptical of this claim and wants to test the hypotheses: Ho: µ =15 versus Ha: µ >15 where  µrepresents the mean increase in scores of  the population of all basketball players who have used the Rose method.  Wesley collects data from an SRS of 25 players who use the Rose method.  He finds that the sample mean increase in scores of these 25 players is 13 points with s=7.  Assuming that the distribution of their scores is approximately normal, what is the p-value for this test?
    • A. 

      0.0830

    • B. 

      0.0228

    • C. 

      0.05 < p-value <0.10

    • D. 

      0.10 < p-value < 0.20

  • 55. 
    Coach Rose claims that by using his method of shooting,  basketball players can increase their scores by an average of 15 points.  Wesley, a  former basketball player is skeptical of this claim and wants to test the hypotheses: Ho: µ = 15 versus Ha:this claim and wants to test the hypothesis: Ha: µ NE 15 where mu represents the mean increase in scores of the population of basketball players who have used the Rose method. Wesley collects data from an SRS of 25 players who use the Rose method. He finds the sample mean increase in scores of these 25 players is 13 points with s=7. The test statistic was computed to be -1.43, what is the p-value for this test?
    • A. 

      0.0830

    • B. 

      0.0228

    • C. 

      0.05 < p-value <0.10

    • D. 

      0.10 < p-value < 0.20

  • 56. 
    A sports scientist took an SRS of twenty five high school basketball players. The scientist then tested their free-throw percentages to estimate the mean free-throw percentage of these players. Here are the data: Stem-and-leaf of free-throw percentages     n=25 Leaf unit = 1.0 On the basis of these data, would you recommend using a one-sample t confidence interval estimate for µ?
    • A. 

      Yes, because an SRS of 25 players was selected.

    • B. 

      Yes, because an SRS was taken and we can assume that free-throw percentages is Normally distributed.

    • C. 

      No, because the t distribution is not robust in this case since there is an outlier.

    • D. 

      No, because no standard deviation is given.

  • 57. 
    True or False: Alpha is the probability of Type I error.
    • A. 

      T

    • B. 

      F

  • 58. 
    True or False:alpha denotes the significance level.
    • A. 

      T

    • B. 

      F

  • 59. 
    True or False:P-value is the probability that the Null hypothesis is false.
    • A. 

      T

    • B. 

      F

  • 60. 
    True or False:Even if the P-value is large, the null hypothesis could be false.
    • A. 

      T

    • B. 

      F

  • 61. 
    True or False:A small P-value means the result have both practical and statistical significance.
    • A. 

      T

    • B. 

      F

  • 62. 
    True or False:Practical significance is only an issue after the results are declared statistically significant.
    • A. 

      T

    • B. 

      F

  • 63. 
    True or False:The t-distribution with df=8 has a smaller spread than the standard normal distribution.
    • A. 

      T

    • B. 

      F

  • 64. 
    True or False:If a p-value is small, then either the null hypothesis is false or we got a very unlikely sample.
    • A. 

      T

    • B. 

      F

  • 65. 
    True or False:Alpha should be large if the consequences of a type I error are very serious.
    • A. 

      T

    • B. 

      F

  • 66. 
    True or False:Margin of error accounts for sampling variability as well as variability due to non-response and measurement error.
    • A. 

      T

    • B. 

      F

  • 67. 
    True or False:The P-value is the probability, computed assuming Ho is true, that the observed outcome would take a value as extreme or more extreme than that actually observed.
    • A. 

      T

    • B. 

      F

  • 68. 
    True or False:We use t procedures for inference on means when the population standard deviation is unknown.
    • A. 

      T

    • B. 

      F

  • 69. 
    True or False:Standard deviation quantifies the variability.
    • A. 

      T

    • B. 

      F

  • 70. 
    True or False:Appropriate collection of data is an important condition for all statistical inferential procedures.
    • A. 

      T

    • B. 

      F

  • 71. 
    Margin of error for a confidence interval for µ
  • 72. 
    Standard deviation of the sampling distribution of  x-bar.
  • 73. 
    Standard error of x-bar.
  • 74. 
    Mean of the sampling distribution of x-bar.
  • 75. 
    Parameter of interest for a matched pair.
  • 76. 
    Confidence interval for the true mean