Question

Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the \(1 \%\) significance level.

State the null and alternative hypotheses.

Short answer

The null and alternative hypotheses are given as,

$$\begin{gathered} H_0:{\mu }_{\text{after}}-{\mu }_{\text{befoe}}\ge 0 \\ {H}_1:{\mu }_{\text{after}}-{\mu }_{\text{before}}<0 \end{gathered}$$

Step-by-step solution

Given information

The table is

Step 2: State the null and alternative hypotheses.

The mean number of balls that were juggled before class was ${\mu }_{\text{before}}$.

Also, the mean number of balls that were juggled after class was ${\mu }_{\text{after}}$.

The null and alternative hypothesis is:

localid="1652950591203" $$\begin{gathered} H_0:{\mu }_{\text{after}}-{\mu }_{\text{befoe}}\ge 0 \\ {H}_1:{\mu }_{\text{after}}-{\mu }_{\text{before}}<0 \end{gathered}$$