Question

Your friend tells you that the proportion of active Major League Baseball players who have a batting average greater than .300 is different from 0.71, a claim you would like to test. The hypotheses for this test are Null Hypothesis: p = 0.71, Alternative Hypothesis: p ≠ 0.71. If you randomly sample 23 players and determine that 14 of them have a batting average higher than .300, what is the test statistic and p-value?

Answer 1

= 14/23 = 0.61

The test statistic z = ( - p)/sqrt(p(1 - p)/n)

                              = (0.61 - 0.71)/sqrt(0.71 * (1 - 0.71)/23)

                              = -1.06

P-value = 2 * P(Z < -1.06)

            = 2 * 0.1446

            = 0.2892