Question 1

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Byron" to test their balls for length and accuracy,but because of swing variations by real golfers,these test robots don't always indicate how the clubs will perform in actual use.One company in the golfing industry is interested in testing its new driver to see if has greater length off the tee than the best-selling driver.To do this,it has selected a group of golfers of differing abilities and ages.Its plan is to have each player use each of the two clubs and hit five balls.It will record the average length of the drives with each club for each player.The resulting data for a sample of 10 players is:  Based on these sample data,what is the point estimate for the difference between the mean distance for the new driver versus the leading driver?
A)2.81
B)1.55
C)-3.45
D)233.4

Accepted Answer

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Question 2

The U.S.Golf Association provides a number of services for its members.One of these is the evaluation of golf equipment to make sure that the equipment satisfies the rules of golf.For example,they regularly test the golf balls made by the various companies that sell balls in the United States.Recently they undertook a study of two brands of golf balls with the objective to see whether there is a difference in the mean distance that the two golf ball brands will fly off the tee.To conduct the test,the U.S.G.A.uses a robot named "Iron Byron," which swings the club at the same speed and with the same swing pattern each time it is used.The following data reflect sample data for a random sample of balls of each brand.  Given this information,what is the test statistic for testing whether the two population means are equal?
A)= 1.115
B)t = 1.96
C)t = -4.04
D)t = -2.58

Accepted Answer

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Question 3

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Mike" to test their balls for length and accuracy,but because of swing variations by real golfers,these test robots don't always indicate how the clubs will perform in actual use.One company in the golfing industry is interested in testing its new driver to see if it has greater length off the tee than the best-selling driver.To do this,it has selected a group of golfers of differing abilities and ages.Its plan is to have each player use each of the two clubs and hit five balls.It will record the average length of the drives with each club for each player.The resulting data for a sample of 10 players are:  What is the critical value for the appropriate hypothesis test if the test is conducted using a 0.05 level of significance?
A)z = 1.645
B)t = 1.7341
C)t = 1.8331
D)t = 2.2622

Accepted Answer

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Question 4

In testing for differences between the means of two paired populations,the null hypothesis is:
A)  :  = 2.
B)  :  = 0.
C)  :  < 0.
D)  :  > 0.

Accepted Answer

The null hypothesis for testing the mean difference between two paired populations is that the difference between the population means is equal to zero. Option B is the only one where the null hypothesis states that the two population means are equal (i.e., difference is zero). Options A, C, and D do not have a null hypothesis stating that the means are equal.

Question 5

Assume that you are testing the difference in the means of two independent populations at the 0.05 level of significance.The null hypothesis is: : - ≥ 0 and you have found the test statistic is z = -1.92.What should you conclude? A)The mean of pop.A is greater than the mean of pop.B because p < α. B)The mean of pop.A is greater than the mean of pop.B because p > α. C)There is no significant difference in the two means because p > α. D)The mean of pop.B is greater than the mean of pop.A because p < α.

Accepted Answer

With a negative test statistic value of -1.92, the p-value is less than the level of significance of 0.05. This leads to the rejection of the null hypothesis. Therefore, we can conclude that the mean of population B is greater than the mean of population A.

Question 6

There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compare with other parts of town.They say that the mean increase from last year to this year has been higher in their part of town than elsewhere.To test this,the assessor's office staff plans to select a random sample of north end properties (group 1)and a random sample of properties from other areas within the city (group 2)and perform a hypothesis test.The following sample information is available:  Assuming that the null hypothesis will be tested using an alpha level equal to 0.05,what is the value of the test statistic?
A)z = 1.578
B)t = 1.7011
C)t = 0.2388
D)t = 0.3944

Accepted Answer

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Question 7

Assume that 10 people join a weight loss program for 3 months.Each person's weight both before and after the program is recorded and the number of pounds each person lost is found.The following summarizes the results for the 10 people: Mean weight lost = 9 pounds
Sample standard deviation of weight lost = 4.6 pounds
Assume that the hypothesis test will be conducted to determine whether or not the weight loss program is effective using a 0.05 level of significance.What is the value of the test statistic?
A)t = 6.19
B)t = 1.96
C)z = 1.96
D)z = 6.19

Accepted Answer

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Question 8

There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compared with other parts of town.They say that the mean increase from last year to this year has been higher in their part of town than elsewhere.To test this,the assessor's office staff plans to select a random sample of north end properties (group 1)and a random sample of properties from other areas within the city (group 2)and perform a hypothesis test.Based on the information provided,the research (or alternate)hypothesis is:
A)  =  .
B)  ≠  .
C)  >  .
D)  <  .

Accepted Answer

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Question 9

In conducting a hypothesis test for the difference in two population means where the standard deviations are known and the null hypothesis is:  :  -  ≥ 0 What is the p-value assuming that the test statistic has been found to be z = 2.52?
A)0.0059
B)0.9882
C)0.0118
D)0.4941

Accepted Answer

The p-value is the probability of getting a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. Since the alternative hypothesis is two-sided, we need to find the area in both tails beyond 2.52 (i.e., the absolute value of the test statistic). Using a standard normal distribution table or calculator, we find the area to be 2*(1 - 0.9941) = 0.0118. Therefore, the p-value is 0.0118.

Question 10

To increase productivity,workers went through a training program.The management wanted to know the effectiveness of the program.A sample of seven workers was taken and their daily production rates before and after the training are shown below.  Based on the data,the training program is
A)effective.
B)ineffective.
C)neither effective nor ineffective.
D)none of the above.

Accepted Answer

From the data, it can be observed that the daily production rates of all workers have increased after the training program. Also, the increase in the production rate is consistent across all workers, indicating that the training program was effective in increasing productivity. Therefore, the best choice is A) effective.

Question 11

The t-test for the mean difference between 2 related populations assumes that the respective:
A)sample sizes are equal.
B)sample variances are equal.
C)populations are approximately normal or sample sizes are large.
D)All of the above.

Accepted Answer

The t-test for the mean difference between 2 related populations assumes that either the populations are approximately normal or the sample sizes are large enough for the central limit theorem to apply. It does not assume equal sample sizes or equal variances. Therefore, option A and B are incorrect. Hence, the correct choice is C.

Question 12

Suppose that a group of 10 people join a weight loss program for 3 months.Each person's weight is recorded at the beginning and at the end of the 3-month program.To test whether the weight loss program is effective,the data should be treated as:
A)independent samples using the normal distribution.
B)paired samples using the t-distribution.
C)independent samples using the t-distribution.
D)independent proportions.

Accepted Answer

Since the weight of each person is recorded at the beginning and end of the program, the data should be treated as paired samples. Paired samples are best analyzed using the t-distribution.

Question 13

There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compare with other parts of town.They say that the mean increase from last year to this year has been higher in their part of town than elsewhere.To test this,the assessor's office staff plans to select a random sample of north end properties (group 1)and a random sample of properties from other areas within the city (group 2)and perform a hypothesis test.The following sample information is available:  Assuming that the null hypothesis will be tested using an alpha level equal to 0.05,what is the critical value?
A)z = 1.578
B)t = 1.7011
C)t = 0.2388
D)t = 2.0484

Accepted Answer

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Question 14

A hypothesis test for the difference between two means is considered a two-tailed test when:
A)the population variances are equal.
B)the null hypothesis states that the population means are equal.
C)the alpha level is 0.10 or higher.
D)the standard deviations are unknown.

Accepted Answer

A two-tailed test is used when the null hypothesis states that the population means are equal, regardless of the population variances or the alpha level.

Question 15

Under what conditions can the t-distribution be correctly employed to test the difference between two population means?
A)When the samples from the two populations are small and the population variances are unknown
B)When the two populations of interest are assumed to be normally distributed
C)When the population variances are assumed to be equal
D)All of the above.

Accepted Answer

The t-distribution can be used to test the difference between two population means when the samples from the two populations are small (less than 30), the population variances are unknown, and/or the two populations of interest are assumed to be normally distributed. Additionally, if the population variances are assumed to be equal, a pooled t-test can be used which provides more accurate results.

Question 16

An advertising company has developed a new ad for one of the national car manufacturing companies.The ad agency is interested in testing whether the proportion of favorable responses to the ad is the same between male adults versus female adults.It plans on conducting the test using an alpha level equal to 0.05.A sample of 100 adults of each gender will be used in the study.Each person will be asked to view the ad and indicate whether they find the ad to be "pleasing" or not.Given this,what is the appropriate null hypothesis?
A)  :  = 
B)  :  ≠ 
C)  :  = 
D)  :  =

Accepted Answer

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Question 17

An advertising company has developed a new ad for one of the national car manufacturing companies.The ad agency is interested in testing whether the proportion of favorable response to the ad is the same between male adults versus female adults.It plans on conducting the test using an alpha level equal to 0.05.A sample of 100 adults of each gender will be used in the study.Each person will be asked to view the ad and indicate whether they find the ad to be "pleasing" or not.Given this information,what is the critical value?
A)z = 1.645
B)t = 1.96
C)z = 1.96
D)Can't be determined without knowing the results of the sample.

Accepted Answer

The critical value for a two-tailed test with an alpha level of 0.05 is 1.96 when using a z-test. Since the sample size is large (n=100) for both male and female adults, a z-test is appropriate. Therefore, the critical value is z = 1.96.

Question 18

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Byron" to test their balls for length and accuracy,but because of swing variations by real golfers,these test robots don't always indicate how the clubs will perform in actual use.One company in the golfing industry is interested in testing its new driver to see how it compares with the best-selling driver.To do this,it has selected a group of golfers of differing abilities and ages.Its plan is to have each player use each of the two clubs and hit five balls.It will record the average length of the drives with each club for each player.Given this description of the planned test,which of the following statements is true?
A)The test won't be meaningful if only five balls are hit by each player with each club.
B)The samples in this case are called paired samples since the same players are hitting both golf clubs.
C)The test will be invalid unless different players are used to hit each club so that the samples will be independent.
D)The samples are independent because each player is independent of the other players.

Accepted Answer

The samples in this case are paired samples because each player is hitting both clubs, and the length of the drives with each club for each player will be compared. Option A is incorrect because the planned test involves taking an average of five balls hit by each player with each club, and this can still provide useful data. Option C is incorrect because using different players to hit each club would make the samples independent, but this isn't necessary for this paired sample test. Option D is also incorrect because the samples are paired, and therefore not independent.

Question 19

If we are testing for the difference between the means of two paired populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to: A)39. B)38. C)19. D)18.

Accepted Answer

When testing for the difference between the means of two paired populations, we use a paired t-test. The formula for the degrees of freedom for a paired t-test is df = n - 1, where n is the sample size. In this case, we have a sample size of 20 for both samples, so the degrees of freedom would be:

df = 20 - 1
df = 19

Therefore, the correct choice is C.

Question 20

Most companies that make golf balls and golf clubs use a one-armed robot named "Iron Byron" to test their balls for length and accuracy,but because of swing variations by real golfers,these test robots don't always indicate how the clubs will perform in actual use.One company in the golfing industry is interested in testing its new driver to see if it has greater length off the tee than the best-selling driver.To do this,it has selected a group of golfers of differing abilities and ages.Its plan is to have each player use each of the two clubs and hit five balls.It will record the average length of the drives with each club for each player.The resulting data for a sample of 10 players are:  What is an appropriate null hypothesis to be tested?
A)  :  = 
B)  :  ≥ 
C)  :  ≤ 0
D)  :  = 0

Accepted Answer

The answer of Most companies that make golf balls and...

Quiz 10: Estimation and Hypothesis Testing for Two Population Parameters

In testing for differences between the means of two paired populations,the null hypothesis is:

Assume that you are testing the difference in the means of two independent populations at the 0.05 level of significance.The null hypothesis is: : - ≥ 0 and you have found the test statistic is z = -1.92.What should you conclude?

In conducting a hypothesis test for the difference in two population means where the standard deviations are known and the null hypothesis is: : - ≥ 0 What is the p-value assuming that the test statistic has been found to be z = 2.52?

To increase productivity,workers went through a training program.The management wanted to know the effectiveness of the program.A sample of seven workers was taken and their daily production rates before and after the training are shown below. Based on the data,the training program is

The t-test for the mean difference between 2 related populations assumes that the respective:

Suppose that a group of 10 people join a weight loss program for 3 months.Each person's weight is recorded at the beginning and at the end of the 3-month program.To test whether the weight loss program is effective,the data should be treated as:

A hypothesis test for the difference between two means is considered a two-tailed test when:

Under what conditions can the t-distribution be correctly employed to test the difference between two population means?

If we are testing for the difference between the means of two paired populations with samples of n1 = 20 and n2 = 20,the number of degrees of freedom is equal to:

If we are testing for the difference between the means of two paired populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to: