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Chapter 10: Q. 59 (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. 42

(a) To test the wear characteristics of two tire brands, A and B, each brand of tire is randomly assigned to 50 cards of the same make and model.

(b) To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

(c) A study was designed to compare the effectiveness of two weight-reducing diets. Fifty obese women who volunteered to participate were randomly assigned into two equal-sized groups. One group used Diet \(A\) and the other used Diet B. The weight of each woman was measured before the assigned diet and

Short Answer

Expert verified

a)Two-samples procedures

b) Paired 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 each value in one sample has an associating value in the other sample, paired ttechniques are used; otherwise, two-sample tprocedures are used.

toperations with two samples

Because each sample contains a different set of tyres.

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

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

toperations that are paired.

Because every subject is represented in both samples.

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 corresponding value in the other, we utilize paired tmethods; otherwise, we use two-sample tprocedures.

toperations with two samples

Because each sample has a large number of individuals,

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Most popular questions from this chapter

Preventing drowning Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

鈥淲ould you marry a person from a lower social class than your own?鈥� Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said 鈥淵es.鈥� Among the 236women, 117said 鈥淵es.鈥�14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1鈮�p2

at the 95%confidence level.

Plan: If conditions are met, I鈥檒l do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student鈥檚 answer to the question should have no relationship to another student鈥檚 answer.
  • Independent The counts of successes and failures in the two groups鈥�91,58,117, and 119鈥�are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z鈮�2.91)鈮�1-0.3982鈮�0.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I鈥檒l reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

42. Long words Mary was interested in comparing the mean word length in articles from a medical journal and an airline鈥檚 in-flight magazine. She counted the number of letters in the first 200 words of an article in
the medical journal and in the first 100 words of an article in the airline magazine. Mary then used Minitab statistical software to produce the histograms shown.

Thirty-five people from a random sample of 125workers from Company A admitted to using sick leave when they weren鈥檛 really ill. Seventeen employees from a random sample of 68workers from Company B admitted that they had used sick leave when they weren鈥檛 ill. A 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren鈥檛 ill is

(a) 0.03卤(0.28)(0.72)125+(0.25)(0.75)68

(b) localid="1650367573248" 0.03卤1.96(0.28)(0.72)125+(0.25)(0.75)68

(c) 0.03卤1.645(0.28)(0.72)125+(0.25)(0.75)68

(d)

0.03卤1.96(0.269)(0.731)125+(0.269)(0.731)68

(e) 0.03卤1.645(0.269)(0.731)125+(0.269)(0.731)68

Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in 7years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.
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