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Chapter 10: Q. 60 (page 658)

Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice. +3

(a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which page in each pair got Ration and which got Ration B.

(b) A random sample of college professors is taken.

We wish to compare the average salaries of male and female teachers.

(c) To test the effects of a new fertilizer, plots are treated with the new fertilizer, and plots are treated with another fertilizer. A computer's random number generator is used to determine which plots get which fertilizer.

Short Answer

Expert verified

a) Paired t procedures

b) Two-sample t procedures

c)Two-sample t procedures

Step by step solution

01

Part (a) Step 1: Given Information

To determine whether paired t-test or two-sample t-test should be used to conduct inference on the basis of the information provided.

02

Part (a) Step 2: Explanation

If a value in one sample has an associating value in another, paired tprocedures are employed; otherwise, two-sample ttechniques are utilized.

toperations that are paired

Because every participant in another sample has a littermate,

03

Part (b) Step 1: Given Information

To determine whether paired t-test or two-sample t-test should be used to conduct inference on the basis of the information provided.

04

Part (b) Step 2: Explanation

When a value in one sample corresponds to a value in the other, paired tmethods are employed; otherwise, two-sample tprocedures are utilized.

toperations with two samples

Because each sample has a large number of individuals,

05

Part (c) Step 1: Given Information

To determine whether paired t-test or two-sample t-test should be used to conduct inference on the basis of the information provided.

06

Part (c) Step 2: Explanation

If a value in one sample has a similar value in the other sample, paired tprocedures are employed; otherwise, two-sample tprocedures are utilized.

toperations with two samples

Because each sample has a variety of people,

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Most popular questions from this chapter

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation 0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20 cups filled with the large setting. Let x1-x炉2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). Find the probability thatx炉1-x炉2 is more than 12 ounces. Show your work.

A quiz question gives random samples of n=10observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9degrees of freedom to calculate a 95%confidence interval for the difference in the two population means. Janelle uses her calculator鈥檚 two-sample t interval with 16.87degrees of freedom to compute the 95%confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

(a) Tom鈥檚 confidence interval is wider.

(b) Janelle鈥檚 confidence interval is wider.

(c) Both confidence intervals are the same.

(d) There is insufficient information to determine which confidence interval is wider.

(e) Janelle made a mistake; degrees of freedom have to be a whole number.

Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anti-clotting drug, named dipyridamole, would be more effective for patients who had already had a stroke. Here are the data on strokes and deaths during the two years of the study.

Number ofpatientsNumber ofstrokesAspirin alone1649206Aspirin + dipyridamole1650157

The study was a randomized comparative experiment.

(a) Is there a significant difference in the proportion of strokes between these two treatments? Carry out an appropriate test to help answer this question.

(b) Describe a Type I and a Type II error in this setting. Which is more serious? Explain

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top 10%of the class will receive an A, the next 20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum average a student could attain and still receive an F for the course?

(a) 70

(b)69.27

(c) 65.75

(d) 62.84

(e)57

Golf club repairs The Ping Company makes custom-built golf clubs and competes in the $4billion golf equipment industry. To improve its business process, Ping decided to study the time it took to repair golf clubs sent to the company by mail. The company determined that 16%of a random sample of orders were sent back to the customers in 5days or less. Ping examined the processing of repair orders and made changes. Following the changes, 90%of a random sample of orders were completed within 5days. Assume that each of the estimated percent is based on a random sample of n orders.

(a) We used the sample data to construct two 90% confidence intervals for the proportion of orders completed within 5 days-one before and one after the changes at Ping. The two intervals are (0.858,0.942) and (0.109,0.211). Find the value of n.

(b) Explain why the interval (0.858-0.211,0.942-0.109)=(0.647,0.833) is not a 95% confidence interval for the improvement in the proportion of orders sent back to customers within 5 days following the change.

(c) Construct and interpret a correct 95% confidence interval to replace the one in part (b).
See all solutions

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