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.

Reject or do not reject Upper H 0 . Choose the correct answer below.

A. Reject Upper H 0 . The population mean is definitely not 39 in. on the basis of these data at a significance level of 0.05.

B. Do not reject Upper H 0 . The population mean is definitely 39 in. on the basis of these data at a significance level of 0.05.

C. Reject Upper H 0 . There is reason to believe that 39 in. is not the population mean at a significance level of 0.05.

D. Do not reject Upper H 0 . There is no reason to believe that 39 in. is not the population mean at a significance level of 0.05.

Answer 1

H₀: = 39

H₁: 39

Test statistic t =

                      

                       = -0.58

For 0.05 significance level the critical value t^* = 2.145

As the test statistic value lies between the critical values (-2.145 < -0.58 < 2.145), we cannot reject the null hypothesis.

Option - B) Do not reject H₀. The population mean is definitely 39 in. on the basis of these data at a significance level of 0.05.