Question

The following table shows the weights (in pounds) and the number of hours slept in a day by a random sample of infants. Test the deithal MX U001. The interpret the results in the context of the problem. If convenient use technology to solve the problem Click the icon to view more information about hypothesis testing for slope. Weight, 81 102 99 73 68 112 11.1 14.9 D Hours slepty 14.8 14.5 142 142 13.7 13.2 13.9 124 Identify the null and alternative hypotheses A. HMX0 HAMO C. HOMO OB. Ho M=0 HA MIO OD. Ho: M20 HAMO HM+0 alculate the test statistic und to three decimal places as needed.)

Answer 1

Solution: The provided sample means are shown below: X = 9.94 X = 13.86 Also, the provided sample standard deviations are: $1 = 2.61 89 = 0.77 and the sample sizes are n = 8 and ng = 8. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Hi H2 Ha: Hi 12 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 = 0.01, and the degrees of freedom are df = 14. 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 t = 2.977, for a = 0.01 and df = 14 The rejection region for this two-tailed test is R = {t: t > 2.977). (3) Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: t- X-X (12-1): +(12-1) 7+12-2 G+) 9.94 13.86 (8-1 2.619+(8-1)0.772 8+8-2 (+3) 4.074 (4) Decision about the null hypothesis Since it is observed that t = 4.074 >te = 2.977, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0011, and since p = 0.0011 <0.01, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean ji is different than 12, at the 0.01 significance level