Question 1

The t distribution has properties similar to the _____ distribution.

Accepted Answer

A) Normal 
B) F 
C) Uniform 
D) None of the above 
A) Normal 
B) F 
C) Uniform 
D) None of the above

Question 2

A simple random sample of 20 third-grade children from a certain school district is selected,and each is given a test to measure his/her reading ability.You are interested in calculating a 95% confidence interval for the population mean score.In the sample,the mean score is 64 points and the standard deviation is 12 points.What is the margin of error associated with the confidence interval?

Accepted Answer

A) 2.68 points 
B) 4.64 points 
C) 5.62 points 
D) 6.84 points 
A) 2.68 points 
B) 4.64 points 
C) 5.62 points 
D) 6.84 points

Question 3

The one-sample z statistic is used instead of the one-sample t statistic when ______.

Accepted Answer

A) F1F1F1S1F1F1F10 is known 
B) F1F1F1S1F1F1F10 is unknown 
C) F1F1F1S1F1F1F10 is known 
D) F1F1F1S1F1F1F10 is unknown 
A) F1F1F1S1F1F1F10 is known 
B) F1F1F1S1F1F1F10 is unknown 
C) F1F1F1S1F1F1F10 is known 
D) F1F1F1S1F1F1F10 is unknown

Question 4

We wish to see if the electronic control indicating the oven temperature for a certain model oven is properly calibrated.Four ovens of this model are selected at random.The electronic control on each is set to 300°F;after 1 hour,the actual temperature of each is measured.The temperatures measured are 305°F,310°F,300°F,and 305°F.Assume that the distribution of the actual temperatures for this model when the electronic control is set to 300°F is Normal.To test if the electronic control is properly calibrated,we will test the following hypotheses: H0: F1F1F1S1F1F1F10 = 300 versus Ha: F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 300.Are the data statistically significant at the 5% significance level?

Accepted Answer

A) Yes,because the P-value is less than 0.05. 
B) Yes,because the sample mean   = 305°F,which is much higher than 300°F. 
C) No,because a difference of 5°F (between   and F1F1F1S1F1F1F10)as compared with 300°F is very small (insignificant). 
D) No,because the P-value is greater than 0.05. 
A) Yes,because the P-value is less than 0.05. 
B) Yes,because the sample mean   = 305°F,which is much higher than 300°F. 
C) No,because a difference of 5°F (between   and F1F1F1S1F1F1F10)as compared with 300°F is very small (insignificant). 
D) No,because the P-value is greater than 0.05.

Question 5

A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago.The sample mean was   = 7 years with a standard deviation of s = 2 years.Assume the distribution of the time the employees have worked for the postal service is approximately Normal.The hypotheses being tested are H0: F1F1F1S1F1F1F10 = 7.5 versus Ha: F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 7.5.A one-sample t test will be used.What is the P-value for the one-sample t test?

Accepted Answer

A) P-value  0.10 
A) P-value  0.10

Question 6

Let n1 represent the sample size of the first group and n2 the sample size of the second group.A t procedure can be used when n1 + n2 is less than ____ if the data are approximately normal.

Accepted Answer

A) 15 
B) 150 
C) 50 
A) 15 
B) 150 
C) 50

Question 7

A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below.   A 95% confidence interval with pooled variance would show a difference in the two group means.

Accepted Answer

A) True 
 B)False

Question 8

A sample of size n = 27 is used to conduct a significance test for H0: F1F1F1S1F1F1F10 = 75 versus Ha: F1F1F1S1F1F1F10 > 75.The test statistic is t = 3.45.What are the degrees of freedom for this test statistic?

Accepted Answer

A) 26 
B) 27 
C) 74 
D) 75 
A) 26 
B) 27 
C) 74 
D) 75

Question 9

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz.Net weights slightly vary from bag to bag.Assume net weights are Normally distributed.A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0: F1F1F1S1F1F1F10 = 14 versus Ha: F1F1F1S1F1F1F10 < 14.To do this,he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each.He finds a sample mean of 13.88 oz with a standard deviation of s = 0.24 oz.Suppose we were not sure if the distribution of net weights were Normal.In which of the following circumstances would the t procedure not be robust in this problem?

Accepted Answer

A) The mean and median of the data are nearly equal. 
B) A histogram of the data is moderately skewed. 
C) A boxplot of the data shows the presence of a large outlier. 
D) The sample standard deviation is large. 
A) The mean and median of the data are nearly equal. 
B) A histogram of the data is moderately skewed. 
C) A boxplot of the data shows the presence of a large outlier. 
D) The sample standard deviation is large.

Question 10

A study was done to determine if students learn better in an online basic statistics class versus a traditional face-to-face (f2f)course.A random sample of 12 students in an online course and 15 students in an f2f course was taken.The scores (out of 100)on the final exam of both groups are shown below.   What are the degrees of freedom for the pooled two-sample t procedure?

Accepted Answer

A) 25 
B) 27 
C) 11 
D) 14 
A) 25 
B) 27 
C) 11 
D) 14

Question 11

A one-sample t test of H0: F1F1F1S1F1F1F10 = 125 against Ha: F1F1F1S1F1F1F10 > 125 is carried out based on sample data from a Normal population.The SRS of size n = 15 produced a mean of   = 132.8 and s = 12.6.What is the value of the appropriate test statistic?

Accepted Answer

A) z = 2.40 
B) t = 2.32 
C) t = 2.40 
D) z = 2.32 
E) t = 1.76 
A) z = 2.40 
B) t = 2.32 
C) t = 2.40 
D) z = 2.32 
E) t = 1.76

Question 12

Twelve runners are asked to run a 10-kilometer race on each of two consecutive weeks.In one of the races,the runners wear one brand of shoe and in the other,a different brand.The brand of shoe they wear in each race is determined at random.All runners are timed and are asked to run their best in each race.The results (in minutes)are given below.   Use the sign test for matched pairs to determine if there is evidence that times using Brand 1 tend to be faster than times using Brand 2.What are the hypotheses we wish to test?

Accepted Answer

A) H0: F1F1F1S1F1F1F10 = 0 versus Ha: F1F1F1S1F1F1F10 > 0,where F1F1F1S1F1F1F10 = the mean of the differences in running times (Brand 2 - Brand 1)for all runners who run this race twice wearing the two brands of shoes 
B) H0: p = 1/2 versus Ha: p F1F1F1S1F1F1F10 1/2,where p = the proportion of running times using Brand 1 that are faster than times using Brand 2 
C) H0: p = 1/2 versus Ha: p > 1/2,where p = the proportion of running times using Brand 1 that are faster than times using Brand 2 
D) H0: population median = 0 versus Ha: population median F1F1F1S1F1F1F10 0,where the median of the differences in running times for all runners who run this race twice wearing the two brands of shoes is measured for Brand 2 - Brand 1 
A) H0: F1F1F1S1F1F1F10 = 0 versus Ha: F1F1F1S1F1F1F10 > 0,where F1F1F1S1F1F1F10 = the mean of the differences in running times (Brand 2 - Brand 1)for all runners who run this race twice wearing the two brands of shoes 
B) H0: p = 1/2 versus Ha: p F1F1F1S1F1F1F10 1/2,where p = the proportion of running times using Brand 1 that are faster than times using Brand 2 
C) H0: p = 1/2 versus Ha: p > 1/2,where p = the proportion of running times using Brand 1 that are faster than times using Brand 2 
D) H0: population median = 0 versus Ha: population median F1F1F1S1F1F1F10 0,where the median of the differences in running times for all runners who run this race twice wearing the two brands of shoes is measured for Brand 2 - Brand 1

Question 13

The hypotheses H0: F1F1F1S1F1F1F10 = 350 versus Ha: F1F1F1S1F1F1F10 < 350 are examined using a sample of size n = 20.The one-sample t statistic has the value t = -1.68.What do we know about the P-value of this test?

Accepted Answer

A) P-value  0.05 
A) P-value  0.05

Question 14

You are interested in determining if the average amount of time (in hours)that students spend on the Internet per day is greater than 2 hours.The data below are from a random sample of 11 students.   The alternative hypothesis for this problem is ______.

Accepted Answer

A) one sided 
B) two sided 
C) three sided 
D) four sided 
A) one sided 
B) two sided 
C) three sided 
D) four sided

Question 15

Ten couples are participating in a small study on cholesterol.Neither the man nor the woman in each couple is known to have any problems with high cholesterol.The researcher conducting the study wishes to use the sign test for matched pairs to determine if there is evidence that the cholesterol level for the husband tends to be higher than the cholesterol level for the wife.The cholesterol measurements for the 10 couples are given below.   What are the hypotheses the researcher wishes to test?

Accepted Answer

A) H0: F1F1F1S1F1F1F10 = 0 versus Ha: F1F1F1S1F1F1F10 > 0,where F1F1F1S1F1F1F10 = the mean of the differences in cholesterol levels (husband - wife)for all couples without cholesterol problems 
B) H0: p = 1/2 versus Ha: p F1F1F1S1F1F1F10 1/2,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife 
C) H0: p = 1/2 versus Ha: p 1/2,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife 
D) H0: population median = 0 versus Ha: population median > 0,where the differences for which the median is calculated are measured as husband - wife 
A) H0: F1F1F1S1F1F1F10 = 0 versus Ha: F1F1F1S1F1F1F10 > 0,where F1F1F1S1F1F1F10 = the mean of the differences in cholesterol levels (husband - wife)for all couples without cholesterol problems 
B) H0: p = 1/2 versus Ha: p F1F1F1S1F1F1F10 1/2,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife 
C) H0: p = 1/2 versus Ha: p 1/2,where p = the proportion of cholesterol levels of the husband that are higher than those of the wife 
D) H0: population median = 0 versus Ha: population median > 0,where the differences for which the median is calculated are measured as husband - wife

Question 16

Two sample t procedures are used when _____.

Accepted Answer

A) subjects are the same in both samples 
B) subjects in one sample are completely unrelated to the subjects in the other sample 
C) subjects are similar in both samples 
D) None of the above 
A) subjects are the same in both samples 
B) subjects in one sample are completely unrelated to the subjects in the other sample 
C) subjects are similar in both samples 
D) None of the above

Question 17

Suppose we were interested in determining if there were differences in the average prices among two local supermarkets.We randomly pick six items to compare at both supermarkets.Which statistical procedure would be best to use for this study?

Accepted Answer

A) Matched-pairs t procedure 
B) One-sample t test 
C) Two-sample t test 
D) None of the above 
A) Matched-pairs t procedure 
B) One-sample t test 
C) Two-sample t test 
D) None of the above

Question 18

A study was to be undertaken to determine if a particular training program would improve physical fitness.An SRS of 31 university students was selected to be enrolled in the fitness program.One important measure of fitness is maximum oxygen uptake.Measurements of oxygen uptake in untrained individuals are known to follow a Normal distribution with a mean of F1F1F1S1F1F1F10F1F1F1S1F1F1F10= 45 mL/kg/min.The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects.The measurements made on the subjects coming into this study produced a mean of   = 47.4 mL/kg/min with a standard deviation of s = 5.3 mL/kg/min.What is the approximate P-value for the test?

Accepted Answer

A) P  0.02 
E) P = 0.0118 
A) P  0.02 
E) P = 0.0118

Question 19

Twelve runners are asked to run a 10-kilometer race on each of two consecutive weeks.In one of the races,the runners wear one brand of shoe and in the other,a different brand.The brand of shoe they wear in each race is determined at random.All runners are timed and are asked to run their best in each race.The results (in minutes)are given below.   Use the sign test for matched pairs to determine if there is evidence that times using Brand 1 tend to be faster than times using Brand 2.What is the (approximate)value of the P-value?

Accepted Answer

A) 0.019 
B) 0.042 
C) 0.05 
D) 0.073 
A) 0.019 
B) 0.042 
C) 0.05 
D) 0.073

Question 20

The sign test is more powerful than the t test.

Accepted Answer

A) True 
 B)False

The t distribution has properties similar to the _____ distribution.

The one-sample z statistic is used instead of the one-sample t statistic when ______.

Let n₁ represent the sample size of the first group and n₂ the sample size of the second group.A t procedure can be used when n₁ + n₂is less than ____ if the data are approximately normal.

A sample of size n = 27 is used to conduct a significance test for H₀:  = 75 versus H_a:  > 75.The test statistic is t = 3.45.What are the degrees of freedom for this test statistic?

A one-sample t test of H₀:  = 125 against H_a:  > 125 is carried out based on sample data from a Normal population.The SRS of size n = 15 produced a mean of = 132.8 and s = 12.6.What is the value of the appropriate test statistic?

The hypotheses H₀:  = 350 versus H_a:  < 350 are examined using a sample of size n = 20.The one-sample t statistic has the value t = -1.68.What do we know about the P-value of this test?

You are interested in determining if the average amount of time (in hours)that students spend on the Internet per day is greater than 2 hours.The data below are from a random sample of 11 students. The alternative hypothesis for this problem is ______.

Two sample t procedures are used when _____.

Suppose we were interested in determining if there were differences in the average prices among two local supermarkets.We randomly pick six items to compare at both supermarkets.Which statistical procedure would be best to use for this study?

The sign test is more powerful than the t test.

Looking at Datadistributions

Looking at Datarelationships

Producing Data

Probability: the Study of Randomness

Sampling Distributions

Introduction to Inference

Inference for Proportions

Inference for Categorical Data

Inference for Regression

Multiple Regression

One-Way Analysis of Variance

Two-Way Analysis of Variance

Logistic Regression

Nonparametric Tests

Bootstrap Methods and Permutation Tests

Statistics for Quality: Control and Capability

Filters

Exam 7: Inference for Means

The t distribution has properties similar to the _____ distribution.

The one-sample z statistic is used instead of the one-sample t statistic when ______.

Let n1 represent the sample size of the first group and n2 the sample size of the second group.A t procedure can be used when n1 + n2 is less than ____ if the data are approximately normal.

A sample of size n = 27 is used to conduct a significance test for H0:  = 75 versus Ha:  > 75.The test statistic is t = 3.45.What are the degrees of freedom for this test statistic?

A one-sample t test of H0:  = 125 against Ha:  > 125 is carried out based on sample data from a Normal population.The SRS of size n = 15 produced a mean of = 132.8 and s = 12.6.What is the value of the appropriate test statistic?

The hypotheses H0:  = 350 versus Ha:  < 350 are examined using a sample of size n = 20.The one-sample t statistic has the value t = -1.68.What do we know about the P-value of this test?

You are interested in determining if the average amount of time (in hours)that students spend on the Internet per day is greater than 2 hours.The data below are from a random sample of 11 students. The alternative hypothesis for this problem is ______.

Two sample t procedures are used when _____.

Suppose we were interested in determining if there were differences in the average prices among two local supermarkets.We randomly pick six items to compare at both supermarkets.Which statistical procedure would be best to use for this study?

The sign test is more powerful than the t test.

Looking at Datadistributions

Looking at Datarelationships

Producing Data

Probability: the Study of Randomness

Sampling Distributions

Introduction to Inference

Inference for Proportions

Inference for Categorical Data

Inference for Regression

Multiple Regression

One-Way Analysis of Variance

Two-Way Analysis of Variance

Logistic Regression

Nonparametric Tests

Bootstrap Methods and Permutation Tests

Statistics for Quality: Control and Capability

Filters

Let n₁ represent the sample size of the first group and n₂ the sample size of the second group.A t procedure can be used when n₁ + n₂is less than ____ if the data are approximately normal.

A sample of size n = 27 is used to conduct a significance test for H₀:  = 75 versus H_a:  > 75.The test statistic is t = 3.45.What are the degrees of freedom for this test statistic?

A one-sample t test of H₀:  = 125 against H_a:  > 125 is carried out based on sample data from a Normal population.The SRS of size n = 15 produced a mean of = 132.8 and s = 12.6.What is the value of the appropriate test statistic?

The hypotheses H₀:  = 350 versus H_a:  < 350 are examined using a sample of size n = 20.The one-sample t statistic has the value t = -1.68.What do we know about the P-value of this test?