The superintendent of a county jail wants to determine how q

The superintendent of a county jail wants to determine how quickly inmates requiring treatment for substance abuse are being moved into a substance abuse facility. For 98 inmates requiring treatment, he determines the mean time to be 70.98 days with standard deviation of 4.3 days.

a. Find the point estimate of the population mean.

b. Obtain the margin of error for 98% confidence.

c. Construct the 98% confidence nterval for the population mean.

Solution

a)

Point estimate = sample mean = 70.98 [ANSWER]

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    70.98          
z(alpha/2) = critical z for the confidence interval =    2.326347874          
s = sample standard deviation =    4.3          
n = sample size =    98          
              
Thus,              
Margin of Error E =    1.010485477   [ANSWER]

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c)

Also,      

Lower bound =    69.96951452          
Upper bound =    71.99048548          
              
Thus, the confidence interval is              
              
(   69.96951452   ,   71.99048548   ) [ANSWER]