Question

Consider the following hypothesis test: H0: ? = 16 Ha: ? ? 16 A sample of 40 provided a sample mean of 14.17. The population standard deviation is 6. a. Compute the value of the test statistic (to 2 decimals). b. What is the p-value (to 4 decimals)? c. Using ? = .05, can it be concluded that the population mean is not equal to 16? Answer the next three questions using the critical value approach. d. Using ? = .05, what are the critical values for the test statistic? (+ or -) e. State the rejection rule: Reject H0 if z is the lower critical value and is the upper critical value. f. Can it be concluded that the population mean is not equal to 16?

Answer 1

a) The test statistic z = ()/()

                                  = (14.17 - 16)/(6/)

                                  = -1.93

P-value = 2 * P(Z < -1.93)

             = 2 * 0.0268

             = 0.0536

c) As the P-value is greater than (0.0536 > 0.05), so we should not reject H₀.

So at = 0.05, it cannot be concluded that the population mean is not equal to 16.

d) At = 0.05, the critical values are z_0.025 = +/- 1.96

e) Reject H₀, if z < -1.96 or z > 1.96

f) As the test statistic value is not less than the lower critical value (-1.93 > -1.96), so we should not reject H_0.

Hence it cannot be concluded that the population mean is not equal to 16.