Question

12. Consider the 2016 rental listings for Manhattan in New York City for non-doorman one bedroom apartments. Suppose that the mean monthly rental for 2016 is $3,500. Suppose that you are interested in whether rental rates for this type of apartment are changing. Your null hypothesis is H₀: μ = $3,500 per month versus H_A: μ ≠ $3,500 per month.

You conduct an SRS of size 60 ads in February for this type of apartment in Manhattan. Your sample statistics:

• x_mean = $3,784
• s = $926

What is the P-value for the hypothesis test (to four decimal places of accuracy)?

Group of answer choices

0.0832

0.0104

0.0208

0.0416

0.1000

13.

Suppose that you have been following the investment advice of your broker. Annual returns on diversified portfolios tend to be close to a Normal distribution. The mean annual total return on an S&P 500 index mutual fund has historically been about 11.95%. However, you suspect that your broker has been giving you bad advice and that your portfolio returns are lower.

Your null hypothesis is H₀: μ = 11.95% per year versus H_A: μ < 11.95% per year.

Your sample statistics for your most recent 15 years of returns:

• x_mean = 9.00%
• s = 23.49%

(Assume that this data approximates a simple random sample.)

What is the P-value for the hypothesis test (to four decimal places of accuracy)?

Group of answer choices

0.4429

0.3171

0.2000

0.1586

0.6342

Answer 1

1.

T- t 3784 – 3500 926/V60 = 2.376 s/n

p value = TDIST(2.376, 59,2) = 0.0208

p value = 0.0208

2.

$t =\frac{ \bar{x} - \mu}{s/\sqrt{n}} =\frac{ 9 - 11.95}{23.49/\sqrt{15}} = -0.486$

p value = TDIST(-0.486, 14,1) = 0.3171

p value = 0.3171