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A community aasciation is interested to estimating the average number of matemit

ID: 3149972 • Letter: A

Question

A community aasciation is interested to estimating the average number of matemity days woman stay in the local hospital. A random sample is taken of 36 women who had babies in the hospital during the past year. The following numbers of maternity days each woman was in the hospital are rounded to the nearest day. Use these data and a population standard deviation of 1.13 to construct a 98% confidence interval to estimate the average maternity stay in the hospital for all woman who have babies in this hospital. (Round the intermediate values to 3 decimal places. Round your answers to 3 decimal places.) mu

Explanation / Answer

Note that              
              
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 =    3.333333333          
z(alpha/2) = critical z for the confidence interval =    2.326347874          
s = sample standard deviation =    1.13          
n = sample size =    36          
              
Thus,              
              
Lower bound =    2.895204484          
Upper bound =    3.771462183          
              
Thus, the confidence interval is              
              
(   2.895204484   ,   3.771462183   ) [ANSWER]

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If you use tables instead of technology, we round z = 2.33.

Note that              
              
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 =    3.333333333          
z(alpha/2) = critical z for the confidence interval =    2.33          
s = sample standard deviation =    1.13          
n = sample size =    36          
              
Thus,              
              
Lower bound =    2.894516667          
Upper bound =    3.77215          
              
Thus, the confidence interval is              
              
(   2.894516667   ,   3.77215   ) [ALTERNATE ANSWER FOR TABLE USE]

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