Question

An automobile manufacturer claims that their car has a 56.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car. After testing 14 cars they found a mean MPG of 56.6 with a standard deviation of 1.1. Is there sufficient evidence at the 0.1 level that the cars underperform the manufacturer's MPG rating? Assume the population distribution is approximately normal. Step 1 of 5: State the null and alternative hypotheses. Answer 2 Points Tables Keypad Keyboard Shortcuts < > Ho Prev Nex H.

Answer 1

The provided sample mean is X = 56.6 and the sample standard deviation is 1.1, and the sample size is n. 14. S = (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: M = 56.7 Ha: μ 7 56.7 This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.1, and the critical value for a two-tailed test is te = 1.771. The rejection region for this two-tailed test is R = {t: \t\ > 1.771} .. (3) Test Statistics The t-statistic is computed as follows: X - μo t= 56.6 – 56.7 1.1/V14 -0.34 s/n (4) Decision about the null hypothesis Since it is observed that t = 0.34 <te = 1.771, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.7392, and since p = 0.7392 > 0.1, 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 u is different than 56.7, at the 0.1 significance level.

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