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: 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?
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?
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?
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?
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?
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?
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?
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?
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?
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.
B.
The sample standard deviation is not large.
C.
There are no outliers nor strong skewness in the data.
D.
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?
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