Question

A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic z = 2.52.

Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points)

Part B: If the alternative hypothesis is Ha: p ≠ 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points) (10 points)

Answer 1

A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic z = 2.52.

Part A:

if = 5 % critical value is 1.64

Conclusion : test statistic z = 2.52 > critical value 1.64 So we reject H0: p = 0.4 with = 5 %

if = 1 % critical value is 2.326

Conclusion : test statistic z = 2.52 > critical value 2.326 So we reject H0: p = 0.4 with = 1 %

Part B: If the alternative hypothesis is Ha: p ≠ 0.4

the test statistic z = 2.52.

if = 5 % critical value is 1.96

Conclusion : test statistic z = 2.52 > critical value 1.96 So we reject H0: p = 0.4 with = 5 %

if = 1 % critical value is 2.58

Conclusion : test statistic z = 2.52 < critical value 2.58 So we do not reject H0: p = 0.4 with = 1 %

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