4. Denise is a professional swimmer who trains, in part, by running. She would l

Question

4. Denise is a professional swimmer who trains, in part, by running. She would like to
estimate the average number of miles she runs in each week. For a random sample
of 20 weeks, the mean is x = 17.5 miles with standard deviation s = 3.8 miles. Find
a 99% confidence interval for the population mean number of weekly miles Denise
runs. 4. __________

(a) 15.01 miles to 19.99 miles (b) 15.07 miles to 19.93 miles
(c) 15.34 miles to 19.66 miles (d) 15.31 miles to 19.69 miles
(e) 15.08 miles to 19.92 miles

Explanation / Answer

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
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 =    0.005          
X = sample mean =    17.5          
t(alpha/2) = critical t for the confidence interval =    2.860934606          
s = sample standard deviation =    3.8          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
Margin of Error E =    2.430952819          
Lower bound =    15.06904718          
Upper bound =    19.93095282          
              
Thus, the confidence interval is              
              
(   15.07 ,   19.93 ) [ANSWER, B]

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