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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

A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected. Each person's weight is recorded before starting the diet and one year after it is concluded. Based on the data shown below (weight in pounds), can we conclude that the diet has a long-term effect, that is, that dieters managed to not regain the weight they lost? Include appropriate statistical evidence to justify your answer.

The elderly fear crime more than younger people, even though they are less likely to be victims of crime. One study recruited separate random samples of 56black women and 63black men over the age of 65from Atlantic City, New Jersey. Of the women, 27said they 鈥渇elt vulnerable鈥� to crime; 46of the men said this.

(a) Construct and interpret a 90%confidence interval for the difference in population proportions (men minus women).

(b) Does your interval from part (a) give convincing evidence of a difference between the population proportions? Explain.

Which of the following is not a property of a binomial setting?

(a) Outcomes of different trials are independent.

(b) The chance process consists of a fixed number of trials,n

(c) The probability of success is the same for each trial.

(d) If we use a sample size of 30, the binomial distribution will be approximately Normal.

(e) Each trial can result in either a success or a failure.

T10.11. Researchers wondered whether maintaining a patient's body temperature close to normal by heating the patient during surgery would affect wound infection rates. Patients were assigned at random to two groups: the normothermic group (patients' core temperatures were maintained at near normal, 36.5掳C, with heating blankets) and the hypothermic group (patients" core temperatures were allowed to decrease to about34.5掳C). If keeping patients warm during surgery alters the chance of infection, patients in the two groups should have hospital stays of very different lengths. Here are summary statistics on hospital stay (in number of days) for the two groups:

Groupnx炉sxNormothemic10412.14.4Hypothermic9614.76.5

(a) Construct and interpret a 95%confidence interval for the difference in the true mean length of hospital stay for normothermic and hypothermic patients.

(b) Does your interval in part (a) suggest that keeping patients warm during surgery affects the average length of patients' hospital staves? Justify your answer.

National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of 143bears measured in a recent year.

Which statement below is correct?

(a) The median will lie in the interval (140,180), and the mean will lie in the interval (180,220).

(b) The median will lie in the interval (140,180), and the mean will lie in the interval (260,300).

(c) The median will lie in the interval (100,140), and the mean will lie in the interval (180,220).

(d) The mean will lie in the interval (140,180), and the median will lie in the interval (260,300).

(e) The mean will lie in the interval (100,140), and the median will lie in the interval (180,200).
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