Question

Independent random samples selected from two normal populations produced the sample means and standard dev atons shown to the right. a. Assuming equal variances, conduct the test Ho: (μι-μ2)-U against Ha: μι-μ2) #0 using α .10. b. Find and interpret the 90% confidence interval for(μ1-μ2) Sample 1 Sample 2 x1 59 x2-7.9 13 2-4.8 a. Find the trst statistic. The test statistic is Round to two decimal places as needed.) ind the p vaue. The p-value is Round to three decimal places as needed.) State the condusipn. Chcase the carrect arswer below. 0 A. Do not reject Hi-There is insufficient evidence that the means differ O B. Raject Ho- There s utfcient evidence that the maans ditter O C. Do n eect H There is sufficient evidenc that the means differ. D. Rect Ho- There is insufficiernt eidenc that the means differ b. The 90% confidence interval for Round to two decimal places as needed. Interpret the confidence interval with 90% confidence, the difference in the means or the two populaions is estimated to fall ..μ.-μ2> (DD evidence to indcate hat frem his inrva. There is that (μ -μ2) differs from. D because the interval

Answer 1

othes The following null and alternative hypotheses need to be tested: 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 a0.1, and the degrees of freedom are df = 26, 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 two-tailed test is te-1.706, for α = 0.1 and df = 26 The rejection region for this two-tailed test is R t>1.706 Since it is assumed that the population variances are equal, the t-statistic is computed as follows: 5.9-7.9 -1.345 17-1)3.12+(11-1)4.81 L 1 17+11-2

Since it is observed that t-1.345 te-1.706, it is then concluded that the null hypothesis is not rejected Using the P-value approach. The p-value is p = 0.1904, and since P = 0.1904 > 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 μ 1 is different than μ2, at the 0.1 significance level. Confidence Interval The 90% confidence interval is-4.537 .:: μι-Ha 0.537