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inna [77]
3 years ago
11

The average size of a new house built in a Hays county in 2010 was 1,872 square feet. A random sample of 40 new homes built in H

ays County were selected in 2014. The average square footage was 2,031 with a standard deviation of 373 square feet. Does this sample provide enough evidence to conclude that the average house size has increased in the Hays County since 2010? Test at an alpha level of 0.05. Find the test statistic.
Mathematics
1 answer:
vlada-n [284]3 years ago
7 0

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:

H_0: \mu = 1872

And the alternate hypothesis is:

H_a: \mu > 1872

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

1872 is tested at the null hypothesis:

This means that \mu = 1872

Sample of 40. The average square footage was 2,031 with a standard deviation of 373 square feet.

This means that n = 40, X = 2031, \sigma = 373

Value of the test-statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{2031 - 1872}{\frac{373}{\sqrt{40}}}

z = 2.7

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.

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