For a study conducted by the research department of a pharmaceutical company, 235 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 $17.80 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 $18.20 with a standard deviation of $4.00 . 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 90% confidence interval for the difference −μ1μ2 between the mean spending on prescription allergy relief medication ( μ1 ) and the mean spending on non-prescription allergy relief medication ( μ2 ). Then find the lower limit and upper limit of the 90% confidence interval.
For a study conducted by the research department of a pharmaceutical company,
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
with a standard deviation of
. A random sample of
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
with a standard deviation of
. 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
confidence interval for the difference
between the mean spending on prescription allergy relief medication (
) and the mean spending on non-prescription allergy relief medication (
). Then find the lower limit and upper limit of the
confidence interval.
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