According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1080 in 2018. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10th to April 15th).

a.A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of Ho will support the researcher's contention.

Ho : u is equal to $1080. Ha : u is less than $1080.

b.For a sample of 400 individuals who filed a tax return between April 10th and 15th, the sample mean refund was $920. Based on prior experience a population standard deviation of o = $1800 may be assumed. What is the p-value (to 4 decimals)?

c.Using a = 0.05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?

d.Repeat the preceding hypothesis test using the critical value approach.

Using a = 0.05, what is the critical value for the test statistic (to 3 decimals)? Enter negative value as negative number.

State the rejection rule: Reject Ho if z is ____________ the critical value.

Using the critical value approach, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?