Researchers at Gallup were interested in whether there was a decrease in the pro

Question

Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people who are not yet retired) who did not believe that the U.S. Social Security program will be able to pay them a retirement benefit when they retire. In the summer of 2010, the Gallup poll found that 60% of nonretirees thought that Social Security would not be able to pay a benefit. Five years later in the summer of 2015, Gallup asked the same question to 1,282 nonretirees and found that 51% of respondents did not think that Social Security would be able to pay a retirement benefit by the time that they retire.

We would like to test the hypothesis that in 2015 there is a lower proportion of nonretirees who do not think that Social Security will be able to pay them a benefit. A z-test for the population proportion showed that z = 4.29, p < 0.001.

Which of the following is the best conclusion based on the output?

We have extremely strong evidence to reject Ha.  

There is a probability of 0 that Ha is correct.  

We have moderately strong evidence to reject H0.  

There is a probability of 0 that H0 is correct.  

We have extremely strong evidence to reject H0.

Explanation / Answer

We decide whether to reject or do not reject the null hypothesis on the basis of test statistic or corresponding p - values. Smaller the p - value would be, stronger we would be having the evidence to reject Ho.

Here, p value os < 0.001 which is very close to 0.

Since p value is very small, We have extremely strong evidence to reject Ho.

Option E is correct.

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