Individuals filing federal income tax returns prior to March 31received an average refund of $1077. Consider the population of\"last-minute\" filers who mail their tax return during the last fivedays of the income tax period (typically April 10 to April 15).

a. A researcher suggests that a reason individuals wait untilthe last five days is that on average these individuals receivelower refunds than do early filers. Develop appropriate hypothesessuch that rejection Ho of will support the researcher'scontention.

Ho: μ is

Hα: μ is

b. For a sample of 400 individuals who filed a tax returnbetween April 10 and 15, the sample mean refund was $920. Based onprior experience a population standard deviation of σ=$1800 may beassumed. What is the p-value (to 4 decimals)?

c. Using , α= 0.05 can you conclude that the population meanrefund for \"last minute\" filers is less than the population meanrefund for early filers? Answer the next three questions using thecritical value approach.

d. Using α= 0.05, what is the critical value for the teststatistic? Enter negative value as negative number. State therejection rule: Reject α= 0.05 if z is ___ the critical value.

Using α= 0.05, can you conclude that the population mean refundfor \"last minute\" filers is less than the population mean refundfor early filers?