Answer :
Answer:
The test statistic is z = 2.7.
The pvalue of the test is 0.0035 < 0.05, which means that this sample provides enough evidence to conclude that the average house size has increased in the Hays County since 2010.
Step-by-step explanation:
The average size of a new house built in a Hays county in 2010 was 1,872 square feet. Evidence that it has increased?
This means that the null hypothesis is:
[tex]H_0: \mu = 1872[/tex]
And the alternate hypothesis is:
[tex]H_a: \mu > 1872[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
1872 is tested at the null hypothesis:
This means that [tex]\mu = 1872[/tex]
Sample of 40. The average square footage was 2,031 with a standard deviation of 373 square feet.
This means that [tex]n = 40, X = 2031, \sigma = 373[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{2031 - 1872}{\frac{373}{\sqrt{40}}}[/tex]
[tex]z = 2.7[/tex]
Pvalue and decision:
The pvalue of the test is the probability of finding a sample mean above 2031. This is 1 subtracted by the pvalue of z = 2.7.
Looking at the z-table, z = 2.7 has a pvalue of 0.9965
1 - 0.9965 = 0.0035
The pvalue of the test is 0.0035 < 0.05, which means that this sample provides enough evidence to conclude that the average house size has increased in the Hays County since 2010.