1. | When is a statistical procedure robust? |
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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: μ_{D}=μ_{T} versus Ha: μ_{D}<μ_{T} . The results of the free-throw shooting skills test are: Two Sample T-test results (without pooled variances): μ_{D}=mean of Deacons μ_{T}=mean of Teachers Ho: μ_{D}-μ_{T} = 0 Ha: μ_{D}-μ_{T} < 0 Difference Sample Mean Std. Err. DF t-stat P-value μ_{D}-μ_{T} -7.31 4.2917 11 -1.5 0.081 On the basis of the P-value, what should we conclude at α=0.10? |
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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? |
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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? |
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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 |
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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 |
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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? |
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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? |
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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? |
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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? |
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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? |
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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? |
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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? |
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14. | Researchers want to compare the mean levels of the good cholesterol and in order to do this, they should perform |
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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? |
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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? |
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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. |
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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. |
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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: |
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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? |
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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? |
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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? |
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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? |
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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? |
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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? |
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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? |
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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 |
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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? |
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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 |
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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? |
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31. | Which one of the following situations will best allow a cause-and-effect conclusion about the relationship between smoking and lung cancer? |
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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/cm^{3}. What is the response variable? |
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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? |
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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 |
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35. | Which one of the following statements best describes the logic of tests of significance? |
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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? |
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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”? |
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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? |
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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? |
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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? |
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41. | In addition to having an SRS, what should be checked in order to validly use the formula when n=15? |
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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? |
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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? |
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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? |
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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? |
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46. | Which of the following questions does a test of significance answer? |
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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? |
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48. | When performing a one-sample t-test of Ho: µ=µ_{o} versus Ha: µ>µ_{o}, the observed effect is equal to the difference between x-bar and µ_{o} (i.e.,x-bar - µ_{o}). For a fixed sample size, if the observed effect were to increase, what would happen to the P-value? |
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49. | When performing a one-sample t-test of Ho: µ=µ_{o} versus Ha: µ>µ_{o}, the observed effect is equal to the difference between x-bar and µ_{o} (i.e.,x-bar - µ_{o}). For a fixed sample size, if the observed effect were to decrease, what would happen to the P-value? |
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50. | The mean percentage free-throw of 12^{th} graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12^{th} 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? |
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51. | The mean percentage free-throw of 12^{th} graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12^{th} 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? |
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52. | The mean percentage free-throw of 12^{th} graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12^{th} 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? |
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53. | The P-value for a significance test is defined as |
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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? |
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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? |
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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? |
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57. | True or False: Alpha is the probability of Type I error. |
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58. | True or False:alpha denotes the significance level. |
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59. | True or False:P-value is the probability that the Null hypothesis is false. |
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60. | True or False:Even if the P-value is large, the null hypothesis could be false. |
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61. | True or False:A small P-value means the result have both practical and statistical significance. |
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62. | True or False:Practical significance is only an issue after the results are declared statistically significant. |
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63. | True or False:The t-distribution with df=8 has a smaller spread than the standard normal distribution. |
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64. | True or False:If a p-value is small, then either the null hypothesis is false or we got a very unlikely sample. |
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65. | True or False:Alpha should be large if the consequences of a type I error are very serious. |
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66. | True or False:Margin of error accounts for sampling variability as well as variability due to non-response and measurement error. |
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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. |
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68. | True or False:We use t procedures for inference on means when the population standard deviation is unknown. |
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69. | True or False:Standard deviation quantifies the variability. |
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70. | True or False:Appropriate collection of data is an important condition for all statistical inferential procedures. |
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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 |