Question

A new prep class was designed to improve SAT test scores. Five students were selected at random. Their scores on two practice exams were recorded, one before the class and one after. The data recorded in the table given below. Are the scores, on average, higher after the class? Test at a $5\%$level.

Short answer

No sufficient evidence is obtained to conclude that the class improves SAT scores significantly at a level of $5\%.$

Step-by-step solution

Given information

Give the scores on two practice tests of five students, one before and after the class.

Calculation

The null and alternative hypothesis is

$$\begin{gathered} H_0:{\mu }_d=0 \\ {H}_a:{\mu }_d>0 \end{gathered}$$

The significant level, $\alpha =5\%=0.05.$

$p-value=0.0874$

The $p-value>0.05$, therefore we do not reject the null hypothesis. As a result, there is insufficient data to infer that the class significantly increases SAT scores at $5\%$significant level.