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. However, according to Nancy Trejos of the Washington Post, the average amount in a 401(k)

plan decreased from $69,200 in 2007 to $50,000 in 2008. 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 and finds a sample average of $51,035.

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 the accounts of those using her managed fund in which you could have 90% confidence.