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Chapter 10: Problem 15

Pizza Hut, after test-marketing a new product called the Bigfoot Pizza, concluded that introduction of the Bigfoot nationwide would increase its sales by more than \(14 \%\) (USA Today, April 2, 1993). This conclusion was based on recording sales information for a random sample of Pizza Hut restaurants selected for the marketing trial. With \(\mu\) denoting the mean percentage increase in sales for all Pizza Hut restaurants, consider using the sample data to decide between \(H_{0}: \mu=14\) and \(H_{a}: \mu>14\). a. Is Pizza Hut's conclusion consistent with a decision to reject \(H_{0}\) or to fail to reject \(H_{0}\) ? b. If Pizza Hut is incorrect in its conclusion, is the company making a Type I or a Type II error?

Short Answer

Expert verified
Pizza Hut's conclusion rejects the null hypothesis (H0) in favor of the alternative hypothesis (Ha). If Pizza Hut's conclusion is incorrect, it is making a Type I error.

Step by step solution

01

Understand the Null Hypothesis

In this case, the Null Hypothesis (H0) signifies that the mean percentage increase in sales for all Pizza Hut restaurants will be equal to 14%
02

Understand the Alternative Hypothesis

The alternative hypothesis (Ha) is that the mean percentage increase in sales for all Pizza Hut restaurants will be greater than 14%.
03

Determine If the Conclusion Rejects the Null Hypothesis

Given Pizza Hut's conclusion that Bigfoot Pizza would increase its sales by more than 14%, it seems that the firm is rejecting the null hypothesis (H0), which stated that the average sales increase would be 14%, in favor of the alternative hypothesis (Ha), which postulates that the average sales increase would exceed 14%.
04

Determine Type of Error

A Type I error occurs when one rejects the null hypothesis when it is true. A Type II error occurs when one fails to reject the null hypothesis when it is false. According to Pizza Hut's conclusion, if it turns out incorrect, the firm is making a Type I error because they are rejecting the true null hypothesis

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Most popular questions from this chapter

Researchers at the University of Washington and Harvard University analyzed records of breast cancer screening and diagnostic evaluations ("Mammogram Cancer Scares More Frequent than Thought," USA Today, April 16,1998 ). Discussing the benefits and downsides of the screening process, the article states that, although the rate of false-positives is higher than previously thought, if radiologists were less aggressive in following up on suspicious tests, the rate of false-positives would fall but the rate of missed cancers would rise. Suppose that such a screening test is used to decide between a null hypothesis of \(H_{0}:\) no cancer is present and an alternative hypothesis of \(H_{a}:\) cancer is present. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) a. Would a false-positive (thinking that cancer is present when in fact it is not) be a Type I error or a Type II error? b. Describe a Type I error in the context of this problem, and discuss the consequences of making a Type I error. c. Describe a Type II error in the context of this problem, and discuss the consequences of making a Type II error. d. What aspect of the relationship between the probability of Type I and Type II errors is being described by the statement in the article that if radiologists were less aggressive in following up on suspicious tests, the rate of false-positives would fall but the rate of missed cancers would rise?

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