A government\'s department of transportation requires tire manufacturers to prov

Question

A government's department of transportation requires tire manufacturers to provide performance information on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the treed wear index, which indicates the tire's resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100. A consumer organization wants to test the actual tread wear index of a brand name of tires that claims "graded 200" on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.6 and a sample standard deviation of 21.8. Complete parts (a) and (b) below. Click here to view page 1 of the table of the critical values of t^1 Click here to view page 2 of the table of the critical values of t^2 a. Is there evidence that the population mean amount is different from a grade of 200? (Use a 0.10 level of significance.) Stale the null and alternative hypotheses. H_0: mu = 200 H_1: mu notequalto 200 Identify the critical value(s). The critical value(s) is(are) 1.7396, 1.7396. (Round to four decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic. The test statistic is - 8563 (Round to four decimal places as needed.) State the conclusion. Do not reject H_0. There is insufficient evidence to conclude the population mean amount is different from a grade of 200. b. Determine the p-value and interpret its meaning. The p-value is ____ (Round to four decimal places as needed.) Interpret the meaning of the p-value. Choose the correct answer below. A. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 4, 400 ounce below 200 if the null hypothesis is false. B. The p-value is the probability of not rejecting the null hypothesis when it is false. C. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 4, 400 ounce above 200 if the null hypothesis is false. D. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 4, 400 ounce away from 200 if the null hypothesis is true. 1: Table of critical values of t

Explanation / Answer

B) P value = P(t<0.8563) + P (t > 0.8563) = 0.4037

Do, P value is 0.4037

Interpret the p value

Option D is correct

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