Answer
$\bar{x}$ = 179 minutes μ=185 minutes,σ=12 minutes,$σ_\bar{s}$$ \frac{12}{$36}$=2, n = 36
α = 0.01, df = 36-1=35, critical value=2.438
t=$ \frac{\bar{x}-μ }{σ_\bar{s}}$
= $ \frac{179-185 }{2}$
=-3
Rejection region = z < -2.438
Non rejection region = z > 2.438
The value z =-3 falls within the rejection region, hence we reject the null hypothesis and claim that the mean duration of nine-inning games has decreased after the meeting.
b. The probability of making a Type I error : α =0.01
c. If the probability of making a Type I error were zero, we failed to reject the null hypothesis , because p-value is always greater than 0 or α.
d. P(Z
