Hypothesis testing for a pharmaceutical company
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A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief,u1 , is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine,u2 . A health insurance company conducted an independent study and collected data from a random sample of 295 individuals for prescription allergy relief medicine. The sample mean is found to be 17.6 dollars/year, with a sample standard deviation of 4.7dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 200 individuals yielded a sample mean of 18.4 dollars/year, and a sample standard deviation of 3.5 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.
null hypothesis:
alternative hypothesis:
type of test statistic:
value of the test statistic rounded to at least three decimal places:
the critical value at the 0.05 level of significance rounded to at least three decimal places:
can we reject the claim that the mean spending on the prescription allergy relief medication is greater than or equal to the mean spending on non prescription allergy medication? yes or no
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Solution Summary
The solution explains how to perform a hypothesis test in the context of a pharmaceutical company.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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