Question

Can someone please explain these questions. I don't understand how you can solve this without knowing standard deviation.

1. A New York real estate firm tracks the cost of apartment rentals in the US. In mid-2002, the nationwide mean apartment rental rate was $895 per month (The Wall Street Journal, July 8, 2002). Have apartment rates increased since then? A sample of 50 apartment rental rates from 2004 resulted in a calculated t statistic of 1.12. Based on this, with a significance level of 0.05, you would conclude that

A) Yes, the sample provides strong evidence to conclude that apartment rates have increased since 2002.

B) No, the sample does not provide evidence that apartment rates have changed since 2002.

C) The p-value is approximately 0.1341.

D) Both B and C.

2. An article in your local newspaper claims that the average time to sell a home in your area is 60 days. You take a sample of 20 homes sold recently and find a 95% confidence interval to be 65 ± 3 days. Your correct conclusion is that:

A) Your sample indicates that all homes take longer than 60 days to sell.

B) Your sample must have been taken incorrectly.

C) You don't see any inconsistency between your confidence interval and the statement in the newspaper.

D) The newspaper article must be incorrect. Your confidence interval indicates that the average time to sell a home is greater than 60 days.

Answer 1

(1)sample size is n = 50

degree of freedom = n-1 = 50-1 = 49

using t distribution table, check t value(1.12) and df(49)

we get

P value = 0.1381

it is clear that this p value is greater than 0.05 significance level, means we failed to reject the hypothesis

option D is correct

(2) 95% confidence interval ranges from (65-2) or 62 to (65+3) or 68. It is clear that the confidence interval lower limit is above 60 days. So, this means that the average time to sell a home is greater than 60.

option D