Question

In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61% called the previous season. A randomly selected umpire called strikes in 2231 of the 3581 pitches (based on data from USA Today). Use a = 0.05. State the hypotheses, check conditions, then find the sample proportion and Z. Include a sketch, state the p-value followed by your conclusion.

Answer 1

Solution :

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.61

H_a : p > 0.61

= x / n = 2231 / 3581 = 0.6230

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.6230 - 0.61 / [(0.61 * 0.39 ) / 3581]

= 1.596

P-value = 0.0552

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that some professional baseball players complained that umpires were calling more strikes than the average rate of 61% called the previous season.