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# Test of hypothesis

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3-10. A researcher interested in the senses of taste and smell has carried out extensive studies in which university students are given each of 20 different foods (apricot, chocolate, cherry coffee, garlic, and so on). She administers each food by dropping a liquid on the tongue. Over the entire student population at her university, the mean number of these 20 foods that students can identify correctly is 14, with a standard deviation of 4. (Let us assume that all the students at this college are tested as a part of a medical screening at the start of each year.) The researcher wants to know whether people's accuracy on this test has more to do with smell or with taste. Thus, she sets up special procedures that keep the person from being able to use the sense of smell during the test. The researcher then tries the procedure on one randomly selected student. This student is able to identify only 5 correctly. Using the .05 significance level, what should the researcher conclude?
Solve this problem explicitly using all five steps of hypothesis testing. Then explain your answer to someone who has never had a course in statistics.

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#### Solution Preview

3-10. A researcher interested in the senses of taste and smell has carried out extensive studies in which university students are given each of 20 different foods (apricot, chocolate, cherry coffee, garlic, and so on). She administers each food by dropping a liquid on the tongue. Over the entire student population at her university, the mean number of these 20 foods that students can identify correctly is 14, with a standard deviation of 4. (Let us assume that all the students at this college are tested as a part of a medical screening at the start of each year.) The researcher wants to know whether people's accuracy on this test has more to do with smell or with taste. Thus, she sets up special procedures that keep the person from being able to use the sense of smell during the test. The researcher then tries the procedure on one randomly selected student. This student is able to identify only 5 correctly. Using the .05 significance level, what should ...

#### Solution Summary

The solution uses five steps of hypothesis testing to test the hypothesis that The mean number of foods that the student can identify using taste alone is less than 14.

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