Question

In Country A, the population mean height for 3-year-old boys is 39 inches. Suppose a random sample of 15 3-year-old boys from Country B showed a sample mean of 38.4 inches with a standard deviation of 4 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Complete parts a through c below.

Find the p-value.

p equals____? (Type an integer or decimal rounded to three decimal places as needed.

Answer 1

Solution:

For the given problem test statistic is:

t= -0.581

P-value= 2*p( t < -0.581)= 2*0.2855= 0.571

4, The provided sample mean is X = 38.4 and the sample standard deviation is s = and the sample size is n = 15. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 39 Ha: uz 39 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 = 0.05, and the critical Based on the information provided, the significance level is a value for a two-tailed test is te 2.145. The rejection region for this two-tailed test is R = {t: 1t| > 2.145} (3) Test Statistics The t-statistic is computed as follows: X — ро 38.4 - 39 t= -0.581 s/ vn 4/V15 (4) Decision about the null hypothesis Since it is observed that \t= 0.581 <tc = 2.145, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.5705, and since p= 0.5705 > 0.05, it is concluded that the null hypothesis is not rejected.