Math / Data & Statistics

QuestionCollege tuition: The mean annual tuition and fees 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 differs from $\$ 35,000$ ? Use the $\alpha=0.01$ level of significance and the $P$ -value method with the TI-84 Plus calculator.
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \mu=35,000 \\ H_{1}: \mu \neq 35,000 \end{array}$
This hypothesis test is a two-tailed $\quad$ test.
Part 2 of 5 (b) Compute the value of the test statistic. Round the answer to two decimal places. $t=1.37$
Part: $2 / 5$
Part 3 of 5 (c) Compute the $P$ -value. Round the $P$ -value to at least four decimal places. $P$ -value $=$ $\square$

Studdy Solution
Use the TI-84 Plus calculator to find the $P$ -value:
1. Press `2nd` then `VARS` to access the `DISTR` menu.
2. Select `tcdf(`.
3. Enter the lower bound as `-1E99`, the upper bound as `-1.37`, and the degrees of freedom as `12`.
4. Press `ENTER` to calculate the left tail $P$ -value.
5. Repeat steps 3 and 4 for the positive $t$ -value `1.37`.
6. Add the two tail probabilities to get the total $P$ -value for the two-tailed test.
The $P$ -value is approximately:
$P\text{-value} = 0.1949$
The $P$ -value is:
$\boxed{0.1949}$

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