Confidence interval for the difference of population means: Use of the standard normal
For a study conducted by the research department of a pharmaceutical company, 290 randomly selected individuals were asked to report the amount of money they spend annually on prescription allergy relief medication. The sample mean was found to be $17.50 with a standard deviation of $5.10. A random sample of 260 individuals was selected independently of the first sample. These individuals reported their annual spending on non-prescription allergy relief medication. The mean of the second sample was found to be $18.50 with a standard deviation of $4.20. As the sample sizes were quite large, it was assumed that the respective population standard deviations of the spending for prescription and non-prescription allergy relief medication could be estimated as the respective sample standard deviation values given above. Construct a 99% confidence interval for the difference M1 -M2 between the mean spending on prescription allergy relief medication (M1) and the mean spending on non-prescription allergy relief medication (M2). Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)
a) What is the lower limit of the 99% confidence interval?
b) What is the upper limit of the 99% confidence interval?