Question

Aurelia, another student, suggested they conduct a significance test to investigate the claim. She tested the hypotheses H0:p=16 versus Ha:p>16 at the significance level of α=0.05 . She obtained a test statistic of 1.83 with a p -value of 0.033 . Do the results of the significance test agree with the results of Clarke’s confidence interval in part (a)? Explain your reasoning.

Answer 1

Answer:

$z = 1.83$

And the p value calculated for the right tailed ted is:

$p_v = 0.033$

The significance level provided for this case is 5% or $\alpha=0.05$. We can see that the p value is lower than this significance level so then we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis and we can conclude that the true parameter of interest for this case is significantly higher than 16. If we find a confidence interval at the same significance level we should get the same results.

Explanation:

for this case she want to test the following system of hypothesis.

Null hypothesis: $p =16$

Alternative hypothesis: $p>16$

And the statistic for this case is given by:

$z = 1.83$

And the p value calculated for the right tailed ted is:

$p_v = 0.033$

The significance level provided for this case is 5% or $\alpha=0.05$. We can see that the p value is lower than this significance level so then we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis and we can conclude that the true parameter of interest for this case is significantly higher than 16. If we find a confidence interval at the same significance level we should get the same results.