Question

A golf instructor is interested in determining if her new technique for improving players' golf scores is effective. She takes four new students. She records their 18 -hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as follows.

The correct decision is

a. Reject$H_0$

b. Do not reject$H_0$

Short answer

The correct decision is (b).

Do not reject$H_0$

Step-by-step solution

Given Information 

The given data is

We have to determine the correct decision .

Explanation 

Let's check the differences from the table: $3,-2,7,1$

We're putting these theories to the test.

${\mu }_D=0,{\mu }_D>0$

The differences' mean and standard deviations are:

$$\begin{gathered} \mu =2.25, \\ s=3.774917 \end{gathered}$$

Computing the test statistic's value:

$$\begin{gathered} t=\frac{\overline{X}}{s}\sqrt{n} \\ =\frac{2.25}{3.774917}\sqrt{4} \\ =1.1921 \end{gathered}$$

The p-value is 0.15946, according to the applet.

We can conclude that we cannot reject hypothesis $H_0$because the p-value is greater than any standard significance level (b).