Question

Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different

baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have

normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball.

State the null and alternative hypotheses.

Short answer

$$\begin{gathered} H_0:{\mu }_{\text{Wesley}}={\mu }_{\text{Rodriguez}} \\ {H}_1:{\mu }_{\text{Wesley}}<{\mu }_{\text{Rodriguez}} \end{gathered}$$

Step-by-step solution

Given information

The table is

Step 2: State the null and alternative hypotheses.

Both baseball pitchers have the same speed, according to the null hypothesis.

Let's say Wesley's average fastball speed is ${\mu }_{\text{wesley}}$.

Let's say Rodriguez's average fastball speed is ${\mu }_{Rodriguez}$.

Below are the null and alternative hypotheses.

$$\begin{gathered} H_0:{\mu }_{\text{wellyy}}={\mu }_{\text{rodrigues}} \\ {H}_1:{\mu }_{\text{welcy}}<{\mu }_{\text{rodrigues}} \end{gathered}$$