Question

B.    Suppose a recent random sample of employees nationwide who have a 401(k)-retirement plan found that 18% of them had borrowed against it in the last year. A random sample of 100 employees from a local company who have a 401(k)-retirement plan found that 14 had borrowed from their plan. Based on the sample results, is it possible to conclude, at the α = 0.025 level of significance, that the local company had a lower proportion of borrowers from its 401(k)-retirement plan than the 18% reported nationwide?

1.       Specify the population parameter of interest:

2.       Formulate the null (H0) and alternate (HA) hypotheses (H0 contains the equality <, >, or = ):

(H0): p

(HA): p

3.       Specify the level of significance (alpha, probability of a Type I error):

4.       What is the value of the test statistic?

5.       What is/are the critical value(s)?

6.       What is the p-value?

7.       Based on the critical value and p-value, do you reject or fail to reject the null? Explain

8.       State your summary statement of the conclusion in non-technical terms, make sure to readdress the original claim.

Answer 1