Question

Realtor Elaine Snyderman took a random sample of 12 homes in a prestigious suburb of

Answer 1

Using the t-distribution, it is found that since the p-value of the test is of 0.0044 < 0.05, it can be concluded that found the average appraised market value is less than $825,000.

The null hypothesis is:

$H_0: \mu = 825000$

The alternative hypothesis is:

$H_1: \mu < 825000$

We have the standard deviation for the sample, thus, the t-distribution is used. 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.

For this problem, the values of the parameters are: $\overline{x} = 780000, \mu = 825000, s = 49000, n = 12$.

The value of the test statistic is:

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

$t = \frac{780000 - 825000}{\frac{49000}{\sqrt{12}}}$

$t = -3.18$

The p-value of the test is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.18 and 12 - 1 = 11 df.

Using a t-distribution calculator, it is of 0.0044.

Since the p-value of the test is of 0.0044 < 0.05, it can be concluded that found the average appraised market value is less than $825,000.

A similar problem is given at brainly.com/question/25369247