Question

ion: The mean annual tuition and fees in the 2013-2014 academic year for a sample of 13 private colleges in California was $38,000 with a standard deviation of $7900. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California is greater than $35,000? Use the =α0.01 level of significance and the critical value method with t

Answer 1

Answer:

The pvalue of the test is of 0.0979 > 0.01, which means that we cannot conclude that the mean tuition and fees for private institutions in California is greater than $35,000.

Step-by-step explanation:

Test if the mean tuition and fees for private institutions in California is greater than $35,000.

This means that at the null hypothesis we test if the fee is of $35,000 or less, that is:

$H_0: \mu \leq 35000$

And at the alternate hypothesis, we test if it is more than this value, that is:

$H_a: \mu > 35000$

The test statistic is:

As we have the standard deviation of the sample, the t-distribution is used.

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

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

35000 is tested at the null hypothesis:

This means that $\mu = 35000$

The mean annual tuition and fees in the 2013-2014 academic year for a sample of 13 private colleges in California was $38,000 with a standard deviation of $7900.

This means that $n = 13, X = 38000, s = 7900$

Value of the test-statistic:

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

$t = \frac{38000 - 35000}{\frac{7900}{\sqrt{13}}}$

$t = 1.37$

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean above 38000, which is the pvalue of t = 1.37, with 13 - 1 = 12 degrees of freedom, using a one-tailed test.

With the help of a calculator, this pvalue is of 0.0979.

The pvalue of the test is of 0.0979 > 0.01, which means that we cannot conclude that the mean tuition and fees for private institutions in California is greater than $35,000.