Hypothesis Testing and Two-Sample Tests and One-Way ANOVA


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Hypothesis Testing and Two-Sample Tests and One-Way ANOVA

QUESTION 1

9-15a

The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 120 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.

At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?

QUESTION 2

9-15b

The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 120 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.

Compute the p-value. Please round to four decimal places.

QUESTION 5

9-25a

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

Using a 0.05 significance level, is there evidence that the population mean amount is different from 8.17 ounces?

QUESTION 6

9-25b

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

Compute the p-value. Please round to four decimal places.

QUESTION 7

9-27a p1

The U.S. Department of Transportation requires tire manufacturers to provide performance information on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the tread wear index, which indicates the tire’s resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100.

A consumer organization wants to test the actual tread wear index of a brand name of tires that claims “graded 200” on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.

Please compute the test statistic (Hint: See formula 9.2). Please round to four decimal places.

QUESTION 8

9-27a p2

The U.S. Department of Transportation requires tire manufacturers to provide performance information on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the tread wear index, which indicates the tire’s resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100.

A consumer organization wants to test the actual tread wear index of a brand name of tires that claims “graded 200” on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.

Using a 0.05 level of significance, please provide the critical value for the appropriate test. Please round to four decimal places.

QUESTION 10

9-27b

The U.S. Department of Transportation requires tire manufacturers to provide performance information on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the tread wear index, which indicates the tire’s resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100.

A consumer organization wants to test the actual tread wear index of a brand name of tires that claims “graded 200” on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.

Please determine the p-value. Please round to four decimal places.

QUESTION 19

9-47a p1

In a recent year, the Federal Communications Commission reported that the mean wait for repairs for AT&T customers was 25.3 hours. In an effort to improve this service, suppose that a new repair service process was developed. This new process, used for a sample of 100 repairs, resulted in a sample mean of 22.3 hours and a sample standard deviation of 8.3 hours.

Please compute the test statistic (Hint: See formula 9.2). Please round to four decimal places.

QUESTION 20

9-47a p2 (Please note this is part b in the textbook)

In a recent year, the Federal Communications Commission reported that the mean wait for repairs for AT&T customers was 25.3 hours. In an effort to improve this service, suppose that a new repair service process was developed. This new process, used for a sample of 100 repairs, resulted in a sample mean of 22.3 hours and a sample standard deviation of 8.3 hours.

Please determine the p-value. Please round to four decimal places.

QUESTION 21

9-47a p3

In a recent year, the Federal Communications Commission reported that the mean wait for repairs for AT&T customers was 25.3 hours. In an effort to improve this service, suppose that a new repair service process was developed. This new process, used for a sample of 100 repairs, resulted in a sample mean of 22.3 hours and a sample standard deviation of 8.3 hours.

Using a 0.05 level of significance, please provide the critical value for the appropriate test. Please round to four decimal places.

QUESTION 23

9-49 p1

You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

Please compute the test statistic (Hint: See formula 10.2). Please round to four decimal places.

QUESTION 24

9-49 p2

You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

Please determine the p-value. Please round to four decimal places.

QUESTION 25

9-49 p3

You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

Using a 0.05 level of significance, please provide the critical value for the appropriate test. Please round to four decimal places.

QUESTION 27

9-55a p1

The U.S. Department of Education reports that 46% of full-time college students are employed while attending college. (Data extracted from “The Condition of Education 2009,” National Center for Education Statistics, nces.ed.gov.) A recent survey of 60 full-time students at Miami University found that 29 were employed.

Please compute the test statistic (Hint: See formula 9.3). Please round to four decimal places

QUESTION 28

9-55a p2

The U.S. Department of Education reports that 46% of full-time college students are employed while attending college. (Data extracted from “The Condition of Education 2009,” National Center for Education Statistics, nces.ed.gov.) A recent survey of 60 full-time students at Miami University found that 29 were employed.

Please determine the p-value. Please round to four decimal places.

QUESTION 29

9-55a p3

The U.S. Department of Education reports that 46% of full-time college students are employed while attending college. (Data extracted from “The Condition of Education 2009,” National Center for Education Statistics, nces.ed.gov.) A recent survey of 60 full-time students at Miami University found that 29 were employed.

Using a 0.05 level of significance, please provide the critical value for the appropriate test. Please round to four decimal places.

QUESTION 61

10-07a

When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and
1,041 for the group that thought about the organic fruit salad. Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.

State the null and alternative hypothesis if you want to determine whether the mean estimated amount of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first

QUESTION 62

10-07b

When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and
1,041 for the group that thought about the organic fruit salad. Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.

In the context of this study, what is the meaning of the Type I error and Type II error?

QUESTION 81

10-21a p1

In industrial settings, alternative methods often exist for measuring variables of interest. The data in Measurements.xls (coded to maintain confidentiality) represent measurements in-line that were collected from an analyzer during the production process and from an analytical lab.

Is there evidence of a difference in the mean measurements in-line and from an analytical lab? Please compute the test statistic (Hint: See formula 10.3). Please round to four decimal places.

QUESTION 82

10-21a p2

In industrial settings, alternative methods often exist for measuring variables of interest. The data in Measurements.xls (coded to maintain confidentiality) represent measurements in-line that were collected from an analyzer during the production process and from an analytical lab.

Is there evidence of a difference in the mean measurements in-line and from an analytical lab? Please determine the p-value. Please round to four decimal places.

QUESTION 83

10-21a p3

In industrial settings, alternative methods often exist for measuring variables of interest. The data in Measurements.xls (coded to maintain confidentiality) represent measurements in-line that were collected from an analyzer during the production process and from an analytical lab.

Is there evidence of a difference in the mean measurements in-line and from an analytical lab? Please provide the critical value for the appropriate test. Please round to four decimal places.

QUESTION 84

10-21a p4

In industrial settings, alternative methods often exist for measuring variables of interest. The data in Measurements.xls (coded to maintain confidentiality) represent measurements in-line that were collected from an analyzer during the production process and from an analytical lab.

Is there evidence of a difference in the mean measurements in-line and from an analytical lab? (Use α = 0.05.)

QUESTION 87

10-23a p1

In tough economic times, the business staff at magazines are challenged to sell advertising space in their publications. Thus, one indicator of a weak economy is the decline in the number of “ad pages” that magazines have sold. The file AdPages.xls contains the number of ad pages found in the May 2008 and May 2009 issues of 12 men’s magazines.

Is there evidence that the mean number of ad pages was higher in May 2008 than in May 2009? Please compute the test statistic (Hint: See formula 10.3). Please round to four decimal places.

QUESTION 88

10-23a p2

In tough economic times, the business staff at magazines are challenged to sell advertising space in their publications. Thus, one indicator of a weak economy is the decline in the number of “ad pages” that magazines have sold. The file AdPages.xls contains the number of ad pages found in the May 2008 and May 2009 issues of 12 men’s magazines.

Is there evidence that the mean number of ad pages was higher in May 2008 than in May 2009? Please determine the p-value. Please round to four decimal places.

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