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Chapter 10: Q.10.126 (page 442)

Measuring Treadwear. R. Stichler et al. compared two methods of measuring treadwear in their paper "Measurement of Treadwear of Commercial Tires" (Rubber Age, Vol. 73:2). Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The data, in thousands of miles, are as follows.

At the5% significance level, do the data provide sufficient evidence to conclude that, on average, the two measurement methods give different results?

Short Answer

Expert verified

The null hypothesis is rejected, and the data are adequate to establish that the two measuring methods provide different findings on average.

Step by step solution

01

Given Information

Given data is shown below

We have to explain Whether the data provide sufficient evidence to conclude that on average the two measurement methods give different result.

02

Explanation

The null and alternative hypothesis are:

H0:渭1=渭2H伪:渭1鈮�渭2

The table is given below:

Mean is:

d炉=鈭�dn=41.311=3.7545

Standard deviation is:

Sd=鈭�di2-鈭�di2nn-1

=258.83-(41.3)21111-1=3.2213

The formula of test statistics is : t=d炉sdm

substitute the given values

t=3.75453.221311

=3.866

The degree of freedom is dof=n-1=11-1=10

The critical value for level of significance is 卤2.228

Since, the value of test statistic is fall in the rejection region.

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Most popular questions from this chapter

Cooling Down. Cooling down with a cold drink before exercise in the heat is believed to help an athlete perform. Researcher 1. Dugas explored the difference between cooling down with an ice slurry (slushy) and with cold water in the article "lce Slurry Ingestion Increases Running Time in the Heat" (Clinical Journal of Sports Medicine, Vol. 21, No, 6, pp. 541-542). Ten male participants drank a flavored ice slurry and ran on a treadmill in a controlled hot and humid environment. Days later, the same participants drank cold water and ran on a treadmill in the same bot and humid environment. The following table shows the times, in minutes, it took to fatigue on the treadmill for both the ice slurry and the cold water.

At the 1%significance level, do the data provide sufficient evidence to conclude that, on average, cold water is less effective than ice slurry For optimizing athletic performance in the heat? (Note; The mean and standard deviation of the paired differences are -5.9minutes and 1.60minutes, respectively.)

Tukey's Quick Test.

In this exercise, we examine an alternative method, conceived by the late Professor John Tukey, for performing a two-tailed hypothesis test for two population means based on independent random samples. To apply this procedure, one of the samples must contain the largest observation (high group) and the other sample must contain the smallest observation (low group). Here are the steps for performing Tukey's quick test.
Step I Count the number of observations in the high group that are greater than or equal to the largest observation in the low group. Count ties as 12.

Step 2 Count the number of observations in the low group that are less than or equal to the smallest observation in the high group. Count ties as 12.

Step 3 Add the two counts obtained in Steps 1 and 2, and denote the sum c.

Step 4 Reject the null hypothesis at the 5% significance level if and only if 肠鈮�7; reject it at the 1% significance level if and only if 肠鈮�10; and reject it at the0.1% significance level if and only
if肠鈮�13.
a. Can Tukey's quick test be applied to Exercise 10.48 on page 416? Explain your answer.
b. If your answer to part (a) was yes, apply Tukey's quick test and compare your result to that found in Exercise 10.48, where a t-test was used.
c. Can Tukey's quick test be applied to Exercise 10.74? Explain your answer.
d. If your answer to part (c) was yes, apply Tukey's quick test and compare your result to that found in Exercise 10.74, where a t-test was used.

Recess and Wasted Food, E. Bergman et al. conducted a study to determine, among other things, the impact that scheduling recess before or after the lunch period has on wasted food for students in grades three through five. Results were published in the online article "The Relationship of Meal and Recess Schedules to Plate Waste in Elementary Schools" (Journal of Child Nutrition and Management, Vol. 28, Issue 2). Summary statistics for the amount of food wasted, in grams, by randomly selected students are presented in the following table.

At the 1%significance level, do the data provide sufficient evidence to conclude that, in grades three through five, the mean amount of food wasted for lunches before recess exceeds that for lunches after recess?

In each of Exercises 10.35-10.38, we have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the pooled t-test and pooled t-interval procedure is reasonable. Explain your answer.

10.38 x1=39.04,s1=18.82,n1=51

x2=49.92,s2=18.97,n2=53

The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months.

At the 5% significance level, do the data provide sufficient evidence to conclude that the meantime served for fraud is less than that for firearms offenses? (Note: x炉1=10.12,s1=4.90,x炉2=18.78, and s2=4.64.)
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