Instructions • State the Ho and H1 • Find the p-value • Conclusion: (a) Reject H
ID: 3256761 • Letter: I
Question
Instructions
• State the Ho and H1
• Find the p-value
• Conclusion: (a) Reject Ho and accept H1 or (b) cannot reject Ho at the desired level of significance.
• Submit software output to support your answers.
• Assume equal variances for two sample
During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.) Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level?
Time
2.98
2.4
2.7
2.25
3.23
3.17
2.93
3.18
2.8
2.38
3.75
3.2
3.27
2.52
2.58
4.45
2.45
Explanation / Answer
H0: The mean time for a game is 3.5 hours, that is = 3.5
Ha: The mean time for a game is less than 3.5 hours, that is < 3.5
Lower-tailed t- test for population mean. a = 0.05
Degrees of freedom = n - 1 = 17 - 1 = 16
Critical t- score = -1.746
Decision Rule: Reject H0 if the test t- score < -1.746
t = (2.96 - 3.5)/0.1358 = -3.9759
Since -3.9759 < -1.746, we reject H0 and accept Ha
Conclusion: It appears that the mean time for a game is less than 3.5 hours.
2.98 2.4 2.7 2.25 3.23 3.17 2.93 3.18 2.8 2.38 3.75 3.2 3.27 2.52 2.58 4.45 2.45 x-bar = 2.96 s = 0.56