Question 1077578: Confidence Intervals: Identify all given stats, indicate what menu (1-prop, T, inference o) and distribution was used.
3. The football coach randomly selects ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 7.0, 10.8, 9.5, 8.0, 11.5, 7.5, 6.4, 11.3, 10.2, 12.6. Assume a normal distribution. Determine a 95% confidence interval for the mean time for all players.
a. Sketch a graph
b. Find the point estimate
c. Construct the interval and find the critical value
d. Find the error
e. How would you rate a player who completes the drill in 8 minutes? Why?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Mean is 9.48 (min), and that is the point estimate
sd is 2.138 min
Do a 1-sample t-test, assume normality and assume s is a reasonable estimator of sigma.
95% CI is mean +/- t(df=9, 0.975)*s/sqrt(n)
t-value (critical value is > |2.62|
SE=2.62*2.138/sqrt(10)=1.53
(7.95, 11.01)
A player who finishes in 8 minutes is considered normal, if the CI is considered a "normal" time. The fact that he is at the lower end if of no significance in this situation. The CI is the range of what the mean could conceivably be at the 95% level for this sample, and that player is in the range. If it were testing a player against 8 minutes, the individual would have a p-value >0.05 and one would not reject Ho.
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