Question

Awe arvey of college students was conducted and found that depend two hours per class hour staying A profee at your school was to determarthe esped you wchool sy different from the two hours. A random sample of fifteen statistics students is came out and the findings indicate an age of 1.5 with devo of 24 hours HO is the will hypothesis and H1 is the alternate hypothesis O ANO 2H - 2

Answer 1

$\\ H0\ is \ \ \mu=2\\ \\ H1\ is \ \ \mu\neq2\\ \\$

The provided sample mean is X = 1.75 and the sample standard deviation is s = 0.24, and the sample size is n = 15. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 2 Ha: u + 2 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 = 0.05, and the critical value for a two-tailed test is te = 2.145. The rejection region for this two-tailed test is R = {t: t > 2.145} (3) Test Statistics The t-statistic is computed as follows: X - μo 1.75 - 2 0.24/15 -4.034 s/n (4) Decision about the null hypothesis Since it is observed that t = 4.034 > tc = 2.145, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p= 0.0012, and since p= 0.0012< 0.05, 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 the population mean u is different than 2, at the 0.05 significance level.