You wish to test the following claim a significance level of =0.005 . Ho:p=0.25

Question

You wish to test the following claim a significance level of =0.005 . Ho:p=0.25 Ha:p<0.25 You obtain a sample of size n=658 in which there are 131 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) greater than 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 less than 0.25. There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.25. The sample data support the claim that the population proportion is less than 0.25. There is not sufficient sample evidence to support the claim that the population proportion is less than 0.25.

Explanation / Answer

here p=0.25 and n=658

std error =(p(1-p)/n)1/2 =0.0169

sample proportion phat=131/658=0.1991

therefore test statistic z=(phat-p)/std error =(0.1991-0.25)/0.0169=-3.016

p value =0.0013

The p-value is  less than

This test statistic leads to a decision to reject the null  

the final conclusion is that. There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.25.

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