Business Statistics in Practice Student Help · From the textbook, Business Statistics in Practice, read the following chapters:
· Hypothesis Testing
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· Decision Theory
CHAPTER 9: Hypothesis Testing
9.1 The Null and Alternative Hypotheses and Errors in Hypothesis Testing
9.2 z Tests about a Population Mean: σ Known
9.3 t Tests about a Population Mean: σ Unknown
9.4 z Tests about a Population Proportion
9.5 Type II Error Probabilities and Sample Size Determination (Optional)
9.6 The Chi-Square Distribution (Optional)
9.7 Statistical Inference for a Population Variance (Optional)
Hypothesis testing is a statistical procedure used to provide evidence in favor of some statement (called a hypothesis). For instance, hypothesis testing might be used to assess whether a population parameter, such as a population mean, differs from a specified standard or previous value. In this chapter we discuss testing hypotheses about population means, proportions, and variances.
In order to illustrate how hypothesis testing works, we revisit several cases introduced in previous chapters and also introduce some new cases:
The Payment Time Case: The consulting firm uses hypothesis testing to provide strong evidence that the new electronic billing system has reduced the mean payment time by more than 50 percent.
The Cheese Spread Case: The cheese spread producer uses hypothesis testing to supply extremely strong evidence that fewer than 10 percent of all current purchasers would stop buying the cheese spread if the new spout were used.
The Electronic Article Surveillance Case: A company that sells and installs EAS systems claims that at most 5 percent of all consumers would never shop in a store again if the store subjected them to a false EAS alarm. A store considering the purchase of such a system uses hypothesis testing to provide extremely strong evidence that this claim is not true.
The Trash Bag Case: A marketer of trash bags uses hypothesis testing to support its claim that the mean breaking strength of its new trash bag is greater than 50 pounds. As a result, a television network approves use of this claim in a commercial.
The Valentine’s Day Chocolate Case: A candy company projects that this year’s sales of its special valentine box of assorted chocolates will be 10 percent higher than last year. The candy company uses hypothesis testing to assess whether it is reasonable to plan for a 10 percent increase in sales of the valentine box.
9.1: The Null and Alternative Hypotheses and Errors in Hypothesis Testing
One of the authors’ former students is employed by a major television network in the standards and practices division. One of the division’s responsibilities is to reduce the chances that advertisers will make false claims in commercials run on the network. Our former student reports that the network uses a statistical methodology called hypothesis testing to do this.
To see how this might be done, suppose that a company wishes to advertise a claim, and suppose that the network has reason to doubt that this claim is true. The network assumes for the sake of argument that the claim is not valid. This assumption is called the null hypothesis. The statement that the claim is valid is called the alternative, or research, hypothesis. The network will run the commercial only if the company making the claim provides sufficient sample evidence to reject the null hypothesis that the claim is not valid in favor of the alternative hypothesis that the claim is valid. Explaining the exact meaning of sufficient sample evidence is quite involved and will be discussed in the next section.
The Null Hypothesis and the Alternative Hypothesis
In hypothesis testing:
1 The null hypothesis, denoted H0, is the statement being tested. Usually this statement represents the status quo and is not rejected unless there is convincing sample evidence that it is false.
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