Question

Suppose the average size of a new house built in a certain county in 2006 was 2 comma 279 square feet. A random sample of 25 new homes built in this county was selected in 2010. The average square footage was 2 comma 198​, with a sample standard deviation of 229 square feet

a. Using alphaequals0.01​, does this sample provide enough evidence to conclude that the average house size of a new home in the county has changed since​ 2006?

b. Use technology to determine the​ p-value for this test.

c. determine the critical values.

d. What conclusion should be drawn

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2279
Alternative Hypothesis, Ha: μ ≠ 2279

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2198 - 2279)/(229/sqrt(25))
t = -1.769

P-value Approach
P-value = 0.0896
As P-value >= 0.01, fail to reject null hypothesis.

Rejection Region
This is two tailed test, for α = 0.01 and df = 24
Critical value of t are -2.797 and 2.797.

There is not sufficient evidence to conclude that the average house size of a new home in the county has changed since​ 2006