A concern of Major League Baseball is that games last too long. Some executives
ID: 3151162 • Letter: A
Question
A concern of Major League Baseball is that games last too long. Some executives in the league's headquarters believe that the mean length of games this past year exceeded 3 hours (180 minutes). To test this, the league selected a random sample of 80 games and found the following results: = 193 minutes and s = 16 minutes.
Based on these results, if the null hypothesis is tested using an alpha level equal to 0.10, which of the following is true?
The null hypothesis should be rejected if xbar > 182.31.
The test statistic is t = 1.2924.
Based on the sample data, the null hypothesis cannot be rejected.
It is possible that when the hypothesis test is completed, a Type II statistical error has been made.
The null hypothesis should be rejected if xbar > 182.31.
The test statistic is t = 1.2924.
Based on the sample data, the null hypothesis cannot be rejected.
It is possible that when the hypothesis test is completed, a Type II statistical error has been made.
Explanation / Answer
std error is 16/sqrt(80)=1.7885.
sample mean has t-dist. with 80-1=79 deg. freedom; from t-table, 1-sided critical value is 1.292
test statistic is (193-180)/1.7885=7.269 (so B false)
reject H0 since test statistic exceeds critical value (so C false)
would reject H0 if sample mean exceeds 180 + 1.292(1.7885)=182.31 (so A true)
type II error is when accept H0 when false - this is always "possible" (so D true)
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