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:
And the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
1872 is tested at the null hypothesis:
This means that
Sample of 40. The average square footage was 2,031 with a standard deviation of 373 square feet.
This means that
Value of the test-statistic:
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.