1 The maternity ward of the Royal Prince of Persia Hospital

1. The maternity ward of the Royal Prince of Persia Hospital is doing a study on the average gestation times of the babies born to its patients. A sample of 45 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 263 days. The population standard deviation of gestation times of all babies is known to be 16 days. It is assumed that this standard deviation will also apply specifically to the patients of the maternity ward of the Royal Prince of Persia Hospital.

Calculate the upper and lower bounds of the 90% confidence interval for the mean gestation time of babies born in the maternity ward of the Royal Prince of Persia Hospital. You may find this standard normal table useful. Give your answers in days to 2 decimal places.

a)Upper bound = days

b)Lower bound = days

2. A sample of 149 Vopstra customers have had their annual phone charge recorded for the previous calendar year. The data were used to calculate a 96% confidence interval for the mean annual phone charge of all Vopstra customers. The confidence interval was calculated as $460

Solution

(1) Given a=1-0.9=0.1, Z(0.05)=1.645(from standard normal table)

So the lower bound is

xbar - Z*s/vn =263-1.645*16/sqrt(45) =259.08

So the upper bound is

xbar + Z*s/vn =263+1.645*16/sqrt(45) =266.92

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(2)you are 96% confident the interval between $400 and $520 contains the mean phone charge of all Vopstra customers