chapter 10 quiz

1. (Points: 0.5)  

 

There are a number of highly touted search engines for finding things of interest on the Internet. Recently, a consumer rating system ranked two search engines ahead of the others. Now, a computer user’s magazine wishes to make the final determination regarding which one is actually better at finding particular information. To do this, each search engine was used in an attempt to locate specific information using specified key words. Both search engines were subjected to 100 queries. Search engine 1 successfully located the information 88 times and search engine 2 located the information 80 times. Using a significance level equal to 0.05, which of the following is true? 

 a. According to the test results, the hypothesis should be rejected since the test statistic value, z = 1.54, falls in the rejection region.

 b. Based the sample data, the null hypothesis of equal population proportions is rejected since the test statistic exceeds the critical value.

 c. Based on the sample data, there is not sufficient evidence to conclude that a difference exists between the proportion of search hits since the test statistic, z = 1.54, does not fall in the rejection region.

 d. Based on the sample data, the null hypothesis should not be rejected since the test statistic of z = 2.04 exceeds the critical value of z = 1.96.

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2. (Points: 0.5)  

 

When performing a hypothesis test for the differerence in the means of two independent populations, where the standard deviations are known, the variances must be assumed equal.

True False

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3. (Points: 0.5)  

 

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account) versus single accounts (one member per account).   To test this, a random sample of checking accounts was selected with the following results:

Single Accounts Joint Accounts

      n = 20        n = 30

      s  = $256        s  = $300

       = $1,123          = $1,245

Based upon these data, the critical value from the t-distribution for testing the difference between the two population means using a significance level of 0.05 is t =  1.6772.        

True False

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4. (Points: 0.5)  

  46. A company in Maryland has developed a device that can be attached to car engines which  they believe will increase the miles per gallon that cars will get.   The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device.   The following data represent the mpg for independent random samples of cars from each population.  The variances are assumed equal and the populations normally distributed.

Given this data, what is the critical value if the owners wish to have a 90 percent confidence interval estimate?   

 a. t = 2.015

 b. t = 1.7823

 c. z = 1.645

 d. z = 1.96

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5. (Points: 0.5)  

 

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account) versus single accounts (one member per account). To test this, a random sample of checking accounts was selected with the following results:Single Accounts Joint Accountsn = 20 n = 30s = $256 s = $300

= $1,123  = $1,245Based upon these data, assuming that the populations are normally distributed with equal variances, the test statistic for testing whether the two populations have equal means is approximately -1.49 .

True False

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6. (Points: 0.5)  

  Suppose a survey is taken of two groups of people where each person is asked a yes/no question, and the proportion of people who answer “yes” is calculated for each group. Which of the following is true about a hypothesis test of the difference in the two proportions?

 a. Normality can be assumed if the sample size for each population is at least 30

 b. Normality can be assumed if, in each group, at least 5 people say yes, and at 5 people say no

 c. The standard deviation must be assumed equal

 d. The t-distribution should be used if the standard deviations are unknown

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7. (Points: 0.5)  

 

In estimating the difference between two population means, if a 95 percent confidence interval includes zero, then we can conclude that there is a 95 percent chance that the difference between the two population means is zero.

True False

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8. (Points: 0.5)  

  A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the store's in-house credit card versus using a Visa, Mastercard, or one of the other major credit cards. To do this, they have randomly selected a sample of customers who have made one or more purchases with each of the types of credit cards. The following represents the results of the sampling:In-House Credit Card National Credit CardSample Size: 86 113Mean Monthly Purchases: $45.67 $39.87Standard Deviation: $10.90 $12.47

Suppose that the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level of .05, what is the value of the test statistic assuming the standard deviations are known?

 a. z = 3.49

 b. z = 11.91

 c. t = 3.49

 d. z = 2.86

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9. (Points: 0.5)  

 

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. All of the above

 c. When the population variances are assumed to be equal.

 d. When the two populations of interest are assumed to be normally distributed

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10. (Points: 0.5)  

 

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers.   They wish to estimate this difference using a 95 percent confidence level. Assume that the variances are equal and the populations normally distributed.   The following data represent independent samples from each population: 

Based on the data given below, the company can conclude that there is a statistical difference between men and women with regard to mean spending at the hardware store with men tending to spend more on average than women.     

True False

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11. (Points: 0.5)  

 

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. They plan 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. Ho: ρ1 = ρ2

 b. Ho: μ1 = μ2

 c. Ho: π1 ≠ π2

 d. Ho: π1 = π2

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12. (Points: 0.5)  

  There are a number of highly touted search engines for finding things of interest on the Internet. Recently a consumer rating system ranked two search engines ahead of the others. Now, a computer user's magazine wishes to make the final determination regarding which one is actually better at finding particular information. To do this, each search engine was used in an attempt to locate specific information using specified key words. Both search engines were subjected to 100 queries. Search engine 1 successfully located the information 88 times and search engine 2 located the information 80 times. Using a significance level equal to 0.05, what is the null hypothesis to be tested?

 a. Ho: π1 ≠ π2

 b. Ho: ρ1 = ρ2

 c. Ho: π1 = π2

 d. Ho: μ1 = μ2

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13. (Points: 0.5)  

 

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. They plan 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. The samples resulted in 57 males that liked the ad and 47 females that liked the ad. Based on this information, what is the value of the test statistic? 

 a. z = 1.645

 b. z = 1.42

 c. t = 2.234

 d. z = 1.024

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14. (Points: 0.5)  

  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, they have selected a group of golfers of differing abilities and ages. Their plan is to have each player use each of the two clubs and hit five balls. They will record the average length of the drives with each club for each player. The resulting data for a sample of 10 players are:

Player New Club Leading Club

1 236.4 237.2

2 202.5 200.4

3 245.6 240.8

4 257.4 259.3

5 223.5 218.9

6 205.3 200.6

7 266.7 258.9

8 240 236.5

9 278.9 280.5

10 211.4 206.5

What is the critical value for the appropriate hypothesis test if the test is conducted using a 0.05 level of significance?

 a. t = 1.7341

 b. t = 1.8331

 c. z = 1.645

 d. t = 2.2622

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15. (Points: 0.5)  

  A recent study posed the question about whether Japanese are managers more motivated than American managers. A randomly selected sample of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.American JapaneseSample Size 211 100Mean SSATL Score 65.75 79.83Population Std. Dev. 11.07 6.41

Which of the following is the correct the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers?

 a. Ho:  A- J = 0 versus H1:  A- J ≠ 0

 b. Ho: μA-μJ = 0 versus H1: μA-μJ ≠ 0

 c. Ho: μA-μJ ≤ 0 versus H1: μA-μJ > 0

 d. Ho: μA-μJ ≥ 0 versus H1: μA-μJ < 0

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16. (Points: 0.5)  

 

A commuter has two different routes available to drive to work. She wants to test whether route A is faster than route B. The best hypotheses are:

 a. Ho : μA - μB< 0 and HA : μA - μB> 0 

 b. Ho : μA - μB> 0 and HA : μA - μB< 0 

 c. Ho : μA - μB< 0 and HA : μA - μB> 0 

 d. Ho : μA - μB = 0 and HA : μA - μB ≠ 0 

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17. (Points: 0.5)  

  36. An accounting firm has been hired by a large computer company to determine whether the proportion of accounts receivables with errors in one division (Division 1) exceeds that of the second division (Division 2). The managers believe that such a difference may exist because of the lax standards employed by the first division. To conduct the test, the accounting firm has selected random samples of accounts from each division with the following results. Division 1 Division 2 Sample size n1 = 100 n2 = 100 Errors found x1 = 13 x2 = 8 Based on this information and using a significance level equal to 0.05, the critical value from the standard normal table is z = 1.645. 

True False

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18. (Points: 0.5)  

 

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. They want 95 percent confidence and will select a sample of 10 men and 10 women for the study. The variances are assumed equal and the populations normally distributed. The sample results are:Men Womenn1 =10 students n2 = 10 students

1 = 2.7 hours  2 = 2.4 hourss1 = .30 hours s2 = .40 hoursBased on these data, the lower limit for the difference between population means is 0.15 hours.

True False

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19. (Points: 0.5)  

 

The t-distribution can be used to test hypotheses about the difference between two population means given the following two assumptions:- each population is normally distributed, and- the two populations have equal variances.

True False

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20. (Points: 0.5)  

  A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers. To test this, the design department manager has selected

a random sample of customers and shown them the first design. A second sample of customers is shown design 2. The manager then asks each customer whether they prefer the new design they were shown over the one they currently own. The following results were observed;Design 1 Design 2Sample size n1 = 150 n2 = 80Number preferring new x1 = 65 x2 = 58

Based on these data and a significance level equal to 0.05, the test statistic is approximately -- 4.22 and thus the null hypothesis should be rejected.

True False

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