6 Inferences Based on a Single Sample
Tests of Hypothesis
Where We’ve Been
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Used sample information to provide a point estimate of a population parameter
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Used the sampling distribution of a statistic to assess the reliability of an estimate through a confidence interval
Where We’re Going
Statistics in Action Diary of a KLEENEX® User—How Many Tissues in a Box?
In 1924, Kimberly-Clark Corporation invented a facial tissue for removing cold cream and began marketing it as KLEENEX® brand tissues. Today, KLEENEX® is recognized as the top-selling brand of tissue in the world. A wide variety of KLEENEX® products is available, ranging from extra-large tissues to tissues with lotion. Over the years, Kimberly-Clark Corporation has packaged the tissues in boxes of different sizes and shapes and varied the number of tissues packaged in each box. For example, currently an upright “Everyday” box contains 80 two-ply tissues, an “anti-viral” box contains 68 tissues (with a moisture-activated middle layer “that kills 99.9% of cold and flu viruses”), and a convenient “On the Go” pack contains 10 miniature tissues.
How does Kimberly-Clark Corp. decide how many tissues to put in each box? According to the Wall Street Journal, marketing experts at the company use the results of a survey of KLEENEX® customers to help determine how many tissues are packed in a box. In the mid-1980s, when Kimberly-Clark Corp. developed a cold-care box, designed especially for people who have a cold, the company conducted its initial survey of customers for this purpose. Hundreds of customers were asked to keep count of their KLEENEX® use in diaries. According to the Wall Street Journal report, the survey results left “little doubt that the company should put 60 tissues in each box.” The cold-care box is now called the “anti-viral” box. The number 60 was “the average number of times people blow their nose during a cold.” The company increased the number of tissues packaged in this box to 68 based on the results of a more recent survey.
From summary information provided in the Wall Street Journal article, we constructed a data set that represents the results of a survey similar to the one just described. In the data file named TISSUES, we recorded the number of tissues used by each of 250 consumers during a period when they had a cold. We apply the hypothesis-testing methodology presented in this chapter to that data set in several Statistics in Action Revisited examples.
Statistics in Action Revisited
Data Set: TISSUES
Suppose you wanted to determine whether the mean level of a driver’s blood alcohol exceeds the legal limit after two drinks, or whether the majority of registered voters approve of the president’s performance. In both cases, you are interested in making an inference about how the value of a parameter relates to a specific numerical value. Is it less than, equal to, or greater than the specified number? This type of inference, called a test of hypothesis, is the subject of this chapter.
We introduce the elements of a test of hypothesis in Sections 6.1–6.3. We then show how to conduct tests of hypothesis about a population mean in Sections 6.4–6.5. Large-sample tests about binomial probabilities are the subject of Section 6.6, and we show how to conduct a test about a population variance in optional Section 6.7. Finally, a nonparametric test for a population median is covered in optional Section 6.8.