Question Determine if the mean tuition of private colleges in California exceeds $\$35,000$ using a one-tailed $t$ -test with $\alpha=0.05$ . $H_0: \mu \leq \$35,000$ $H_a: \mu > \$35,000$

Studdy Solution

STEP 1

Assumptions1. The mean annual tuition and fees for a sample of23 private colleges in California is $38,500. . The standard deviation of the sample is$ 7700.
3. The population of private colleges in California is approximately normal.
4. We are testing whether the mean tuition and fees for private institutions in California is greater than $35,000.<br />5. We are using the$ \alpha=0.05 $level of significance.<br />6. We are using the$ $-value method with the TI-84 Plus calculator.

STEP 2

State the null hypothesis. The null hypothesis is the statement that we are trying to find evidence against. In this case, the null hypothesis is that the mean tuition and fees for private institutions in California is $35,000.
$H0 \mu = \$35,000$

STEP 3

State the alternate hypothesis. The alternate hypothesis is the statement that we are trying to find evidence for. In this case, the alternate hypothesis is that the mean tuition and fees for private institutions in California is greater than $35,000.
$H_a \mu > \$35,000$ Here, $\mu$ represents the population mean annual tuition and fees for private colleges in California.

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