Question

You wish to test the following claim a significance level of α = 0.05 . H o : p = 0.5 H a : p > 0.5 You obtain a sample of size n = 461 in which there are 257 successful observations.

What is the test statistic for this sample? test statistic = Round to 3 decimal places.

What is the p-value for this sample? P-value = Use Technology Round to 4 decimal places.

The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.5.

There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.5. The sample data support the claim that the population proportion is greater than 0.5.

There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.5.

Answer 1

Test hypothesis Ho: p=0.5 H2:p<0.5 (claim) Given sample size n=461, x =257 Sample proportion p = * =257 = 0.5575 n 461 Test statistic z=_ Ñ-p p(1-p)/n =- 0.5575-0.5 0.5(1-0.5)/461 = 2.468 P-value=P(22.468)=0.0068 Since p-value< 0.05 hence reject the null hypothesis The sample data support the claim that the population proportion is greater Than 0.5