Question

a new prep class was designed to improve sat test scores. four students were selected at random. their scores on two practice exams were recorded, one before the class and one after. the data recorded in table 10.18. are the scores, on average, higher after the class? test at a 5% level. sat scores student 1 student 2 student 3 student 4 score before class 1840 1960 1920 2150 score after class 1920 2160 2200 2100 table 10.18 • write null and alternative hypotheses. is this one or two - tailed test?

Explanation:

Step1: Define the null and alternative hypotheses

Let \(\mu_d=\mu_{\text{after}}-\mu_{\text{before}}\) (the population mean of the differences).
The null hypothesis \(H_0:\mu_d = 0\) (no improvement, i.e., the mean score after is not higher than the mean score before).
The alternative hypothesis \(H_1:\mu_d> 0\) (scores are higher on average after the class).

Step2: Determine the type of test

Since the alternative hypothesis has a \(>\) sign (we are only interested in whether the scores are higher after the class, not lower or different in either direction), this is a one - tailed test.

Answer:

The null hypothesis \(H_0:\mu_d = 0\), the alternative hypothesis \(H_1:\mu_d>0\). This is a one - tailed test.