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:
And at the alternate hypothesis, we test if it is more than this value, that is:
The test statistic is:
As we have the standard deviation of the sample, the t-distribution is used.
In which X is the sample mean, 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
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
Value of the test-statistic:
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.