Question

College tuition:

The mean annual tuition and fees in the 2013 - 2014 academic year for a sample of 15 private colleges in California was 32,500 with a standard deviation of $7250. A dotplot shows that it is reasonable to assume that the population that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California is less than 35,000? Use a = 0.05 level of significance and the critical value method.

The hypothesis is a ... test.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 35,000
Alternative hypothesis: u < 35,000

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1871.942
DF = n - 1

D.F = 14
t = (x - u) / SE

t = - 1.336

t_critical = - 1.761

Rejection region is t < - 1.761

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Interpret results. Since the t-value (-1.761) is does not lies in the critical region, hence we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the mean tuition and fees for private institutions in California is less than 35,000.