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, py, is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, uy. A health insurance company conducted an independent study and collected data from a random sample of 210 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 285 individuals yielded a sample mean of 18.3 dollars/year, and a sample standard deviation of 4.4 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.

Answer 1

given, n=210, x Da =285, X -230.05 = 17. 7 6 = 5.6 = 18:3, Sa = 4:ý Nall Salternative hypothesis iss Holl, lla Hielly Lelle Type of test : one toiled (left taited) 2- test statistics is. Z = (x-2) (17.7 -183) 715-692 14:41)? - 0.6 0.9661 2x Z : -1.287 Critical value = -1064 Rejection / acceptanco regikon Region A -1.287 -1287 -1.64 0 Hence, we fail to rejeet Ho Conclusion: No, we can not reject the claim