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Confidence interval for the difference of population means: Z test
For a study conducted by the research department of a pharmaceutical company, 295 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 $17.70 with a standard deviation of $4.30. A random sample of 250 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 $18.30 with a standard deviation of $3.50. 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 95% confidence interval for the difference between M1 - M2 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 95% confidence interval?
b) What is the upper limit of the 95% confidence interval?
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What is (are) the mode(s)? Does it make sense to talk about the average for this data? Why or why not?
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