An agent for a real estate company wanted to predict the monthly rent for apartm

Question

An agent for a real estate company wanted to predict the monthly rent for apartments based on the size of the apartment. The data for a sample of 25 apartments is available below. Perform a t test for the slope to determine if a significant linear relationship between the size and the rent exists.

a. At the 0.05 level of significance, is there evidence of a linear relationship between the size of the apartment and the monthly rent?

b. Construct a 95% confidence interval estimate of the population slope, 1.

Size_(sq._ft)      Rent_($)

840                         1925

1440                       2600

1085                       2200

1222                       2525

718                         1975

1495                       2700

1126                       2675

736                         1925

710                         1900

956                         2175

1090                       2375

1295                       2675

1975                       3325

1379                       2825

1175                       2400

1215                       2475

1235                       2100

1259                       2725

1150                       2225

896                         2150

1371                       2600

1030                       2675

765                         2200

1010                       1800

1200                       2775

a. Determine the hypotheses for the test. (Choose the correct answer below)

A. H0: 1 =0

H1: 1 0

B. H0: 1 0

H1: 1 <0

C. H0: 1 0

H1: 1 >0

D. H0: 0 =0

H1: 0 0

Find the test statistic. (Fill in the Blanks)

tSTAT = ___? (Round to two decimal places as needed.)

What is the p-value?

p-value = ____?(Round to three decimal places as needed.)

Reach a decision. (Choose Below)

(Do not reject, Reject) H0. There is (sufficient, insufficient) evidence to conclude that there is a linear relationship between the size of the apartment and the monthly rent.

(Fill in the Blanks)

b. The 95% confidence interval is ___? 1 ___?. (Round to four decimal places as needed.)

Explanation / Answer

a)   

option

A. H0: 1 =0

H1: 1 0 is correct

b) tStat = 7.5328844

p-value = 0.0000001185

since p-value is less than 0.05

we reject the null and conclude that There is sufficient, evidence to conclude that there is a linear relationship between the size of the apartment and the monthly rent.

b)   The 95% confidence interval is   0.78623924618   1 .   1.38155120

0.7862 <1 .   1.3816

Please rate my solution

Size_(sq._ft) Rent_($) 840 1925 1440 2600 1085 2200 1222 2525 718 1975 1495 2700 1126 2675 736 1925 710 1900 956 2175 1090 2375 1295 2675 1975 3325 1379 2825 1175 2400 1215 2475 1235 2100 1259 2725 1150 2225 896 2150 1371 2600 1030 2675 765 2200 1010 1800 1200 2775

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