Question

Suppose the average size of a new house built in a certain county in 2006 was 2,273 square feet. A random sample of 30 new homes built in this county was selected in 2010. The average square footage was 2,185 with a sample standard deviation of 229 square feet.

a.	Using α equals=0.10 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.

a. Determine the null and alternative hypotheses. Choose the correct answer below.

A.

H0​: μ=2,273 and H1​:μ≠2,273

B.

H0​: μ≥2,273 and H1​: μ<2,273

C.

H0​: μ=2,273 and H1​: μ>2,273

D.

H0​: μ≠2,273 and H1​: μ=2,273

Determine the critical​ value(s).

The critical​ value(s) is(are) ____

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test​ statistic,

t Subscript x overbartx.

t Subscript x overbartx = _____

​(Round to two decimal places as​ needed.)

What conclusion should be​ drawn? Choose the correct answer below.

A. Reject the null hypothesis. The data do not provide sufficient evidence to conclude that the average house size has changed since 2006.

B. Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the average house size has changed since 2006.

C. Do not reject the null hypothesis. The data provide sufficient evidence to conclude that the average house size has changed since 2006.

D. Reject the null hypothesis. The data provide sufficient evidence to conclude that the average house size has changed since 2006.

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

​p-value = _____

​(Round to three decimal places as​ needed.)

Answer 1

Here in this Question it is given that the average size of a new house built in a certain county in 2006 was 2,273 square feet. A random sample of 30 new homes built in this county was selected in 2010. The average square footage was 2,185 with a sample standard deviation of 229 square feet.

Now our claim is that the average house size of a new home in the county has changed since​ 2006.

a. The null and alternative hypotheses.

A.0​: μ=2,273 and H1​:μ≠2,273

Now to test this claim we have to use one sample t test because here the population standard deviations is unknown.

Further the one sample t test is performed at 0.10 level of significance as below,

The t critical value is calculated using t table or using Excel. At two tailed t,0.05,30-1 = +-1.699.

b) The critical​ value(s) is(are) -1.699, +1.699.

c) t Subscript x overbartx = -2.105.

d) Conclusion : since p value is less than alpha level of significance so we fail to Reject null hypothesis. At 0.10 level of significance.

D. Reject the null hypothesis. The data provide sufficient evidence to conclude that the average house size has changed since 2006.

e) The p value is calculated using t table or using Excel,

P value= 0.044.