Many companies have moved employee retirement plans to ones based on 401(k) savings. In fact, most large mutual fund companies, like Vanguard, offer 401(k) options.
According to US News and World Report, the amount in an average plan depends not only on the age of the participant but also on the person’s salary range. For someone in his or her 50s making between $60,000 and $80,000, the 401(k) plan would contain $226,266. A local investment advisor, seeing this figure, thinks those using her managed fund have more than the reported amount. She selects a random sample of 55 in that income range and finds a sample average of $241,387.
a. If the standard deviation for the amount in the investors’ accounts is $1,734.23, determine if the investment advisor is correct in her assumption that those she is advising have more than the reported average amount. Use a significance level of 0.025 and discuss any assumptions you made to answer this question.
b. Determine the largest plausible average balance for the accounts of those using her managed fund in which you could have 90% confidence.