Question

Suppose the following data were collected relating the selling price of a house to square footage and whether or not the house is made out of brick. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average brick houses are more expensive than other types of houses at the 0.050.05 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."

Selling Prices of Houses
Price	Sqft	Brick (1 if brick, 0 if otherwise)
233345	3526	0
244243	3427	1
210353	2717	1
215363	2919	0
166225	1342	0
212661	2838	1
205273	2507	1
222408	2884	1
151125	1650	0
167933	1908	0
242592	3516	1
240660	3399	1
192820	2080	1
199901	2497	0
170040	1515	0
238768	3503	1
226069	3263	0
186387	2258	0
204800	2495	1
214960	2772	0

how do you arrived to the answer?

Correct Answer:PRICEi=106558.07+36.61SQFTi+7398.16BRICKi+ei

Answer 1

Solution:-

The regression equation is Y = 106558.0743 + 36.61*X₁ + 7398.16*X₂

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁> u₂
Alternative hypothesis: u₁ < u₂

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 10860.772
DF = 18

t = [ (x₁ - x₂) - d ] / SE

t = - 2.61

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of -2.61

Therefore, the P-value in this analysis is 0.009.

Interpret results. Since the P-value (0.009) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that that on average brick houses are more expensive than other types of houses at the 0.05 level of significance.