Question

For a study conducted by the research department of a pharmaceutical company,

265

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

$4.40

. A random sample of

205

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

$3.70

. 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

−μ1μ2

between the mean spending on prescription allergy relief medication (

μ1

) and the mean spending on non-prescription allergy relief medication (

μ2

). 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.)

Answer 1

1 = 17.7

2 = 18.3

1 = 4.4

2 = 3.7

n1 = 265

n2 = 205

= 0.05

From Table, critical values of Z = 1.96

Confidence Interval:

(17.7 - 18.3) (1.96 X 0.3740)

= - 0.6 0.7330

= ( - 1.33 ,0.13)

Confidence Interval:

- 1.33 < < 0.13