Question

11) Is there a significant difference at a = 0.10 in the average heights in feet of high towers in Europe and the ones in South Africa? The data are shown. 497 463 888 Europe 1236 1288 1312 987 365 South Africa 714 705 964 1227 325 830 369 721 1799

please solve without using the P value. Include a bell graph.

Answer 1

Solution: The provided sample means are shown below: X = 879.5 X = 850.44 Also, the provided sample standard deviations are: 81 = 392.27 89 = 449.89 and the sample sizes are n = 8 and ng = 9. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Mi = 12 Ha: Huo 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 = 0.10, and the degrees of freedom are df = 14.998. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal: Hence, it is found that the critical value for this two-tailed test is t = 1.753, for a=0.10 and df = 14.998. The rejection region for this two-tailed test is R = {t: t > 1.753}. (3) Test Statistics Since it is assumed that the population variances are unequal, the t-statistic is computed as follows: X1 - X2 ta V ni 879.5 - 850.44 = 0.142 392.272 + 449.892 V (4) Decision about the null hypothesis Since it is observed that t = 0.142 <te = 1.753, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.8888, and since p= 0.8888 >0.10, 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 41 is different than at the 0.10 significance level.