Question

According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,463 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 49 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,640 square feet with a sample standard deviation of 66 square feet. Calculate the value of the test statistic.

Answer 1

Using the t-distribution, it is found that the value of the test statistic is t = -87.3.

At the null hypothesis, it is tested if the mean is of 2,463 square feet, that is:

$H_0: \mu = 2463$

At the alternative hypothesis, it is tested if the mean is smaller, that is:

$H_1: \mu < 2463$.

We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

The parameters are:

• $\overline{x}$ is the sample mean.

• $\mu$ is the value tested at the null hypothesis.

• s is the standard deviation of the sample.

• n is the sample size.

The values of the parameters are: $\overline{x} = 1640, \mu = 2463, s = 66, n = 49$.

Hence, the value of the test statistic is:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{1640 - 2463}{\frac{66}{\sqrt{49}}}$

$t = -87.3$

To learn more about the t-distribution, you can take a look at brainly.com/question/25819230