A growing number of younger employees have been participating in their company’s retirement plans in recent years. According to Vanguard Group, 44% of employees under the age of 25 were making contributions to their 401(k) plans in 2011 (compared to just 27% in 2003). A random sample of 340 employees under the age of 25 was recently selected, and it was found that 167 of them made contributions to their 401(k) plans this year.

a. Using σ = 0.01, perform a hypothesis test to determine if the percentage of employees under the age of 25 who have made contributions to their 401(k) plan is more than 44%.

b. Determine the p value for this test and interpret its meaning.

c. Verify your results using PHStat.

d. How would the conclusions be affected if you chose to use σ = 0.05 rather than σ = 0.01.