Case Closed Testing Claims

AP STATISTICS | SHUBLEKA | CASE CLOSED: I’m getting a headache!  

The makers of Aspro brand aspirin want to be sure that their tablets contain the right amount of active ingredient (acetylsalicylic acid). So they inspect a sample of 36 tablets from a batch of production. When the production process is working properly, Aspro tablets have an average of μ = 320 milligrams (mg) of acetylsalicylic acid with a standard deviation of σ = 3 mg. Here are the amounts (in mg)of acetylsalicylic acid in the 36 selected tablets. 319 328 321 324 322 320 324 321 320 324 322 317 319 316 320 325 326 316 316 326 318 322 320 321 319 321 322 319 326 320 324 320 318 321 322 318

What do these data tell us about the mean acetylsalicylic acid content of the tablets in the batch? Should the company distribute these tablets to drugstores or dispose the entire batch?

1. Does it matter what method was used to select the sample of 36 tablets? Explain. 2. What null and alternative hypotheses would you recommend testing? Be sure to justify your choice of a one-sided or two-sided test. 3. Describe a Type I and a Type II error in this setting, and give a possible consequence of each. 4. Which significance level would you recommend: 0.10, 0.05, or 0.01? Justify your answer. 5. Carry out a significance test. What conclusion would you draw about this batch of tablets? 6. Construct a confidence interval to estimate the true mean acetylsalicylic acid content in this batch of Aspro tablets. Use a confidence level that corresponds to the significance level you chose in question 4. In fact, these data were generated from a Normal distribution with μ = 321 and σ = 3 . 7. Use technology to calculate the power of your test from Question 5. Then explain two ways the company could have increased the ability of the test to detect a 1 mg difference from the target μ = 320 mg. 8. Write a brief report toe Aspro executives summarizing your findings.