Question

A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief,

μ1

, is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine,

μ2

. A health insurance company conducted an independent study and collected data from a random sample of

235

individuals for prescription allergy relief medicine. The sample mean is found to be

17.7

dollars/year, with a sample standard deviation of

5.6

dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of

275

individuals yielded a sample mean of

18.3

dollars/year, and a sample standard deviation of

4.5

dollars/year. Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above. Is there sufficient evidence to reject the claim made by the research department of the company, at the

0.05

level of significance? Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we reject the claim that the mean spending on prescription allergy relief medication is greater than or equal to the mean spending on non-prescription allergy relief medication? Yes No

μ σ p x s p

Answer 1

H₀:  ​​​​​​>_{​​​​​​}

H₁:  

The test statistic is z.

Z = ()/

= (17.7 - 18.3)/sqrt((5.6)^2/235 + (4.5)^2/235)

= -1.280

P-value = P(Z < -1. 280)

= 0.1003

Sing the p-value is greater than the significance level (0.1003 > 0.05), so we should not reject the null hypothesis.

No, we cannot reject the claim that the mean spending on prescription allergy relief medication is greater than or equal to the mean spending on non-prescription allergy relief medication

.