The maternity ward of the Royal Prince of Machupicchu Hospital is doing a study

Question

The maternity ward of the Royal Prince of Machupicchu Hospital is doing a study on the average gestation times of the babies born to its patients. A sample of 55 past patients in the ward have been randomly selected and the gestation times of their babies recorded. The sample mean gestation time was calculated as 264 days. The population standard deviation of gestation times of all babies is known to be 15 days. It is assumed that this standard deviation will also apply specifically to the patients of the maternity ward of the Royal Prince of Machupicchu Hospital. Calculate the upper and lower bounds of the 95% confidence interval for the mean gestation time of babies born in the maternity ward of the Royal Prince of Machupicchu Hospital. Give your answers in days to 2 decimal places. a) Upper bounddays b) Lower bounddays

Explanation / Answer

a) Upper bound = 267.96

b) Lower bound = 260.04

CI for 95% n 55 mean 264 z-value of 95% CI 1.9600 std. dev. 15 SE = std.dev./sqrt(n) 2.02260 ME = z*SE 3.96422 Lower Limit = Mean - ME 260.03578 Upper Limit = Mean + ME 267.96422 95% CI (260.0358 , 267.9642 )

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