Question

A random sample of 121 observations from a population with standard deviation 50 yielded a sample mean of 120. (a.)Test the null hypothesis that μ= 110 against the alternative hypothesis that μ >110, using α=.05 Interpret the results of the test. (b.)Test the null hypothesis thatμ= 110 against the alternative hypothesis thatμ6= 110, using α=.05 Interpret the results of the test. (c.)compare the p−values of the two tests you conducted. Explain why the results differ.

Answer 1

(a) The hypothesis being tested is:

H₀: µ = 110

H_a: µ > 110

The test statistic, t = (x - µ)/s/√n

t = (120 - 110)/50/√121

t = 2.2

The p-value is 0.0149.

Since the p-value (0.0149) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ > 110.

(b) The hypothesis being tested is:

H₀: µ = 110

H_a: µ ≠ 110

The test statistic, t = (x - µ)/s/√n

t = (120 - 110)/50/√121

t = 2.2

The p-value is 0.0297.

Since the p-value (0.0297) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ ≠ 110.

(c) The p-value for the part (b) is double because the distribution's tail is on the both sides.