The Little League Association is interested in determining the average distance

Question

The Little League Association is interested in determining the average distance a male T-ball player can throw a T-ball. The data below represents the distance thrown in yards for twenty randomly selected male T-ball players.

a. Estimate the average distance a male T-ball player can throw a T-ball.

b. Estimate with 95% confidence the average distance a male T-ball player can throw a T-ball.

c. The Little League Association has claimed in the past that male T-ball players can throw a T-ball farther than fifteen yards. At 95% confidence, is their claim correct?

Explanation / Answer

a)

Using the technology to get the sample mean,

X = sample mean =    15.7   [ANSWER]

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b)      

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    15.7          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
s = sample standard deviation =    4.780442613          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
              
Lower bound =    13.46268399          
Upper bound =    17.93731601          
              
Thus, the confidence interval is              
              
(   13.46268399   ,   17.93731601   ) [ANSWER]

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c)

NO, there is no evidence that it is correct, because part of the confidence interval is less than 15 yards.

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