In: Statistics and Probability
2. A researcher believes that smoking affects a person’s sense of smell. To test this, he takes a sample of 25 smokers and gives them a test of olfactory sensitivity. In this test, higher scores indicate greater sensitivity. For his sample, the mean score on the test is 14.8 with a standard deviation of 2.4. The researcher knows the mean score in the population is 16.2, but the population standard deviation is unknown.
(a) What are the null and alternative hypotheses in this study (stated mathematically)?
(b) Should the researcher use a one-tailed or a two-tailed test? (c) Compute the appropriate test statistic for testing the hypothesis.
(d) Using α = 0.01, do you conclude that smoking affects a person’s sense of smell? Be sure to include a discussion of the critical value in your answer.
(e) What type of error might the researcher be making in part (d)?