Question

is this correct?

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type lovens is greater than the repair cost for type Il ovens. A sample of 47 type I ovens has a mean repair cost of $75.51, with a standard deviation of $23.53. A sample of 54 type Il ovens has a mean repair cost of $71.32, with a standard deviation of $18.43. Conduct a hypothesis test of the technician's claim at the 0.01 level of significance. Let be the true mean repair cost for type I ovens and be the true mean repair cost for type Il ovens. Step 1 of 4: State the null and alternative hypotheses for the test. Answer 2 Points Tables Keypad HOME 42 Ne H.H > M2

Answer 1

Solution: The provided sample means are shown below: X1 = 75.51 X = 71.32 Also, the provided sample standard deviations are: $1 = 23.53 S2 = 18.43 and the sample sizes are ni = 47 and n2 = 54. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Mi = 2 Ha: Mi > M2 This corresponds to a right-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 = 0.01, and the degrees of freedom are df = 99. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: Hence, it is found that the critical value for this right-tailed test is te = 2.365, for a = 0.01 and df = 99. The rejection region for this right-tailed test is R = {t:t> 2.365) (3) Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: X1 X2 (n-1) +(12-1) (1 +1) 75.51 - 71.32 (47-123.539 +(54-1) 18.431 = = 1.002 1 (4) Decision about the null hypothesis Since it is observed that t = 1.002<te = 2.365, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.1593, and since p = 0.1593 > 0.01, 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 greater than mo, at the 0.01 significance level.