Problem 2 At a particular university in an urban area, official policy mandates that university-owned student...

Problem 2

At a particular university in an urban area, official policy mandates that university-owned student housing shall rent for no more than 80% of the market rate for comparable housing. Rent for all two-bedroom university-owned student apartments is $570/month. All the university-owned two-bedroom student apartments have one bathroom, no view, and are comparable in construction, size, age, amenities, etc. To determine whether the rent satisfies the rules, an administrator proposes to compile as complete a list as he can of two-bedroom apartments for rent in the area, using sources including newspaper ads, commercial rental listing services, and bulletin boards. Then, he will take a simple random sample of 150 of the apartments in the list, and visit each one to determine whether it is comparable to the university-owned apartments in size, number of bathrooms, state of repair, amenities (such as laundry facilities, bathtub/shower), etc. He will compute the sample mean rent of those apartments he finds to be comparable to the university-owned apartments. Let r denote the mean rent of all comparable two-bedroom apartments in the area, and let R denote the sample mean rent of the comparable two-bedroom apartments the administrator finds. The administrator will approach the problem of determining whether the university is complying with the mandate as an hypothesis test.

Suppose that the administrator finds that 36 of the apartments are comparable to two-bedroom university-owned student apartments. Assume that

  • these 36 apartments can be treated as a random sample of size 36 with replacement from the population of comparable two-bedroom apartments for rent in the area, and
  • the distribution of rents for comparable apartments in the area is approximately normal.

Suppose that the sample mean of the rents is $732 and the sample standard deviation of the rents is $116.

a) The estimated standard error of the sample mean is $ ____?

b) The number of degrees of freedom for Student's t-curve to approximate the probability histogram of the T statistic is ______?

c) The observed value of the T statistic is _____?

d) The P-value of the null hypothesis is _____?

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