Question

Consider a two tailed hypothesis test. The null and alternative hypotheses are presented below Ho 100 H1 : μ 100 a. Suppose the test statistic1.44. Find the p-value of the test and the critical value for the test when α-001. Then show that the conclusion using the critical value approach will be identical to the conclusion based on the p-value b. Now suppose the test statistic is ะ-_301. Find the p-value of the test and the critical value for the test when a0.01. Then show that the conclusion using the critical value approach will be identical to the conclusion based on the p-value c. Does the 95% confidence interval include the value 100? Explain your answer.

Answer 1

Solution

(a) Z = 1.44

p value ( 2 tailed) = 0.1499

do not reject the null as p value > $\alpha$

critical value at +-0.005 = 2.576

do not reject null hypothesis as z critical value > z test statistic

(b) z = -3.01

p value = 0.0026

Reject the null hypothesis as p value < $\alpha$

Z critical value = -2.576

Reject null hypothesis as z critical value < z test statistic

(c) Yes, as 95% CI = (100 +- margin of error)