A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine. A health insurance company conducted an independent study and collected data from a random sample of 275 individuals for prescription allergy relief medicine. The sample mean 17.6 is found to be dollars/year, with a sample standard deviation 5.2 of dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 240 individuals yielded a sample mean of 18.4 dollars/year, and a sample standard deviation of 4.0 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 0.01 level of significance? Perform a one-tailed test. Then fill in the table below.
State the null hypothesis?
State the alternate hypothesis?
State the type of test statistic?
State the critical value or 0.01 level of significance?