Question

In a recent survey conducted by pew research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does the same evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of Significance.

1. State the null and the alternative hypothesis?

2. What type of hypothesis test is to be used?

3. What distribution should be used and why?

4. Is this a right, left, or two-tailed test?

5. Compute the test statistic?

6. Compute the p-value?

7. Do you reject or not reject the null hypothesis? Explain why.

8. What do you conclude?

Answer 1

Given

n=295

X=156

P0=0.5

Alpha = 0.05

p=x/n. = 156/295 =0.5288

1) H0: P=0.5. V/s. H1 : P > 0.5

2) we have to use one proportion z test.

3) standard normal distribution because test statistic follw standard normal distribution.

4)Right tailed test

5)test statistic

Z=​​​​​​

Z=​​​​​​

Z= 0.99

6) p-value = p(z >Z)

=p(z > 0.99) = 0.1611

7)

P-value > alpha

Fail to reject null hypothesis.

8) there is not sufficient evidence to conclude that the majority of Americans without a high school diploma are worried about having enough saved for retirement.