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 401(k) balance was $ 85,200. Assume the population standard deviation is $ 21,000. Using σ = 0.02, answer the following:

a. State the null and alternative hypothesis.

b. What conclusions can be made about the current average balance of 401(k) accounts?

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

d. Verify your results using PHStat.

e. If σ = 0.05 had been used rather than σ = 0.02, would the conclusions differ? Comment on this choice of alpha.