Question

The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more. A company that is running a career fair decides to take a random sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127.
Required:
Do the data provide statistically significant evidence at the 0.06 kevel that the average teaching stay in the metro Atlanta area is greater than the state average?

Answer 1

Answer:

The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.

Step-by-step explanation:

The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more.

At the null hypothesis, we test if they pay the average, that is:

$H_0: \mu = 48553$

At the alternate hypothesis, we test if they pay more, that is:

$H_1: \mu > 48553$

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.

48553 is tested at the null hypothesis:

This means that $\mu = 48553$

Sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127.

This means that $n = 228, X = 49021, \sigma = 3127$

Value of the test statistic:

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

$z = \frac{49021 - 48553}{\frac{3127}{\sqrt{228}}}$

$z = 2.26$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 49021, which is 1 subtracted by the p-value of z = 2.26.

Looking at the z-table, z = 2.26 has a p-value of 0.9881

1 - 0.9881 = 0.0119

The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.