Question

In a recent year, some professional baseball player complained that umpires were calling more strikes than the rate of 61% called the previous year. At one point in the season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA Today). Use a 0.10 significant level to test the claim that Morrison’s strike rate is higher than 61%.

Answer 1

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We are given that pcap = x/n = 2231/3581 =0.62301

p = .61

Now, lets calcualate the p-value. If p-value is less than .10 then we will conclude that the claim that Morrison' strike rate is higher than 61% is CORRECT. If p-value is more than .10 then we can't conclude so for lack of evidence.

Now, let's formulate the hypothesis in the following way:

Ho: p = .61

Ha: p > 0.61 ( claim)

p-value = P(p > .61). Standardizing:

P(Z> (pcap-p)/sqrt(p*p'/n))

= P(Z> (.62301-.61)/sqrt(.61*.39/3581))

= P(Z> 1.596)

= 1- P(Z<=1.596) [this we get from the Z-tables]

= 0.0552

This is less than alpha of .10 . We reject Ho, and say that the claim is correct.

Answer: We reject the null hypothesis and conclude that the claim that Morrison’s strike rate is higher than 61% is CORRECT