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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

Refer again to Fig. 10.8 on page 427, where each pair of graphs shows the distributions of a variable on two populations. Suppose that, in each case, you want to perform a small-sample hypothesis test based on independent simple random samples to compare the means of the two populations. In each case, decide which, if any, of the following tests is preferable: the pooled t-test, the non pooled t-test, or the Mann-Whitney test. Explain your answers.

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

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.

Identify the assumption for using the two means ztest and the two mean zinterval procedure that renders those procedures generally impractical.

In Exercises 10.25-10.30, hypothesis tests are proposed. For each

hypothesis test,

a. identify the variable.

b. identify the two populations,

c. determine the null and alternative hypotheses.

d. classify the hypothesis test as two-tailed, left-tailed, or right-tailed.

Teaching Duties. Contingent faculty members in higher education are non-tenure track faculty, adjuncts, postdocs, lecturers, of instructors. R. Bowden and L. Gonzalez researched whether contingent faculty members are different from tenure-track faculty members with regards to teaching, research, and service in the article "The Rise of Contingent Faculty: Its Impact on the Professoriate and Higher Education" (Journal of Applied Research in Higher Education, Vol. 4, No. 1, pp. 5-22). A hypothesis test was conducted to decide whether the mean number of classes taught for credit per semester was less for contingent faculty than for tenure-track faculty.
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