Question

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Q5) 2 points Engineers at a large automobile manufacturing company are trying to decide whether to purchase brand A or brand B tires for the company's new models. To help them arrive at a decision, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are as follows: Brand A: = 37,900 kilometers, S1 = 5100 kilometers. Brand B: 12 = 39,800 kilometers, S2 = 5900 kilometers. Test the hypothesis that there is no difference in the average wear of the two brands of tires. Assume the populations to be approximately normally distributed with equal variances. Use a P-value.

Answer 1

and the sample sizes are ni 12 and n2 12. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Mi = M2 Ha: Mi * M2 This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the degrees of freedom are df = 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: 2.074, for Hence, it is found that the critical value for this two-tailed test is te 0.05 and df = 22. a = The rejection region for this two-tailed test is R={t:1t| > 2.074}. (3) Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: t = X1 – X2 (n1-1)sí +(n2–1) sź ( 1 +1) ni+n2-2 ni n2 37900 – 39800 -0.844 (12-1)51002+(12-1)59002 ( 1 (12 12+12-2 + 1) (4) Decision about the null hypothesis Since it is observed that |t| = 0.844 <tc = 2.074, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p= 0.4078, and since p=0.4078 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean Mi is different than um, at the 0.05 significance level.

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