Homework Sourse1 A growing number of younger employees have been participat
1) A growing number of younger employees have been participating in their company\'s retirement plans in recent yeras. 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 alpha = .01, perform a hypothesis test to determin if the percentage of employees under the age of 25 who have made contributions to their 401 k plan is more than 44%.
2) According to Fidelity Investments, the average 401 K account balance was $77,300 in 2013. To test if this average has recently changed, suppose a sample of 30,401 k plans was recently selected, and it was found that the average was $85,200. Assume the population standard deviation is $21,000. Using alpha = 0.02, answer the following:
A) State the null and alternative hypothesis. For this question follow and show the 7 steps for hypothesis testing.
B) What conclusions can be made about the current average balance of 401 k accounts?
Solution
1)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.44
Ha: p > 0.44
As we see, the hypothesized po = 0.44
Getting the point estimate of p, p^,
p^ = x / n = 0.491176471
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.026920362
Getting the z statistic,
z = (p^ - po)/sp = 1.901032047
As this is a 1 tailed test, then, getting the p value,
p = 0.028648908
significance level = 0.01
Comparing p and the significance value, we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the percentage of employees under the age of 25 who have made contributions to their 401 k plan is more than 44%. [CONCLUSION]
