Question

98. The tail area above a test statistic value of z- 1.812 is 0.035. Determine whether each of the following statements is true or false. A) If the alternative hypothesis is of the form Ha: μ> μ , the data are statistically significant at significance level α 0.05. B) If the alternative hypothesis is of the form Ha: μ > μ, the data are statistically significant at significance level α-0.10. C) If the alternative hypothesis is of the form Ha: o, the data are statistically significant at significance level α-0.05. D) If the alternative hypothesis is of the form Ha: μ μο, the data are statistically significant at significance level a 0.10.

Can someone explain each part of this?

Answer 1

The tail area above z = 1.812 is 0.035

A) The hypothesis is one sided and as p-value = 0.035 < $\alpha$ = 0.05, we reject the null hypothesis.

The data are statistically significant at $\alpha$ = 0.05.

B) The hypothesis is one sided and as p-value = 0.035 < $\alpha$ = 0.10, we reject the null hypothesis.

The data are statistically significant at $\alpha$ = 0.10.

C) The hypothesis is two sided and p-value = 0.035 +0.035 = 0.07.

As p-value = 0.07 > $\alpha$ = 0.05, we fail to reject the null hypothesis.

The data are not statistically significant at $\alpha$ = 0.05.

D) The hypothesis is two sided and p-value = 0.035 +0.035 = 0.07.

As p-value = 0.07 < $\alpha$ = 0.10, we reject the null hypothesis.

The data are statistically significant at $\alpha$ = 0.05.