Procter & Gamble (P&G) merged with Gillette in 2005. One of the concerns the new, larger company has is the increasing burden of retirement expenditures. An effort is being made to encourage employees to participate in 401(k) accounts. Nationwide, 66% of eligible workers participate in these accounts. The file titled Gillette contains responses of 200 P&G workers when asked if they were currently participating in a 401(k) account.
a. Determine the sample proportion of P&G workers who participate in 401(k) accounts.
b. Determine the sampling error if in reality P&G workers have the same proportion of participants in 401(k) accounts as does the rest of the nation.
c. Determine the probability that a sample proportion at least as large as that obtained in the sample would be obtained if P&G workers have the same proportion of participants in 401(k) accounts as does the rest of the nation.
d. Does it appear that a larger proportion of P&G workers participate in 401(k) accounts than do the workers of the nation as a whole? Support your response.