Over a period of about nine months 1353 women reported the t

Over a period of about nine months, 1,353 women reported the timing of each of their menstrual cycles. For the first cycle reported by each woman, the mean cycle time was 28.86 days, and the standard deviation of the 1,353 times was 4.24 days.

a) construct a 99% confidence interval for the population mean cycle time

b) because environmental rhythms can influence biological rhythms, one might hypothesize that the population mean menstrual cycle times is 29.5 days, the length of the lunar month. Is the confidence interval of part (a) consistent with this hypothesis?

Solution

a)

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 =    0.005          
X = sample mean =    28.86          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    4.24          
n = sample size =    1353          
              
Thus,              
Lower bound =    28.5630837          
Upper bound =    29.1569163          
              
Thus, the confidence interval is              
              
(   28.5630837   ,   29.1569163   ) [ANSWER]

*********************

B)

No, as 29.5 is not inside the interval. [ANSWER]