SOLUTION: 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,

Question 1153179: 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)?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: mu is greater than or equal to 16.2
Ha: mu is less than 16.2
alpha is 0.05 P{reject Ho|Ho true}
one tail test because suspect difference will only be less.
test stat is a t df=24 0.95
critical value is t<-1.711
t=(14.8-16.2)/2.4/sqrt(25)
t=-1.4*5/2.4=-2.92
reject Ho because t is less than the critical value of -1.711. There is evidence to support the claim that the mean is less than 16.2 in smokers.
Can make a Type I error, of rejecting the Ho given that it might be true, although the probability is small (0.0038)
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