Use the following information to answer the next five...

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. table cannot copy State the null and alternative hypotheses.

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.
table cannot copy
State the null and alternative hypotheses.

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Key Concepts

Null Hypothesis

The null hypothesis is the default assumption that there is no difference between the means of the two populations. It states that any observed differences are due to random sampling variability rather than a true difference in the population means.

Alternative Hypothesis

The alternative hypothesis proposes that there is a true difference between the means of the two populations. In a directional or one-tailed test, it specifically suggests that the mean of one population is greater than the mean of the other.

Two-Sample Comparison

When comparing the means of two separate groups or populations, a two-sample comparison is used. This method assumes that the samples are independent and, in many cases, that the underlying data are normally distributed, enabling the use of tests like the two-sample t-test.

One-Tailed Test

A one-tailed test is used when the research hypothesis predicts a specific direction of the effect. It tests whether the mean of one population is significantly greater (or smaller) than the mean of another, thereby focusing the statistical test on one end of the distribution.

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