Question

college tuition: the mean annual tuition and fees for a sample of 22 private colleges in california was $33,750 with a standard deviation of $7400. 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 less than $35,000? use the α = 0.05 level of significance and the p - value method with the ti - 84 plus calculator.
part 1 of 5
(a) state the null and alternate hypotheses.
h0: □
h1: □
this hypothesis test is a select ▼ test.
part 2 of 5
(b) compute the value of the test statistic. round the answer to at least two decimal places.
t = □

Explanation:

Step1: Identify the hypothesis test type

Since we are testing if the mean tuition and fees is less than a certain value, it is a one - tailed (left - tailed) \(t\) - test. The null hypothesis \(H_0\) is the statement of no difference or the status quo. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for.
The formula for the \(t\) - test statistic is \(t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean under the null hypothesis, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Given \(\bar{x} = 33750\), \(\mu=35000\), \(s = 7400\), \(n = 22\)

Step2: Calculate the \(t\) - test statistic

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Answer:

The value of the test statistic \(t\approx - 0.79\)