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Chapter 10: Problem 40

Step 2 of the five-step process for hypothesis testing is selecting an appropriate method. What is involved in completing this step?

Short Answer

Expert verified
Completing step 2 of the hypothesis testing involves determining the appropriate statistical test to use based on factors such as the nature of the data, scale of measurement, sample distribution and size, and the type of analysis.

Step by step solution

01

Understanding Hypothesis Testing

The basis for completing this step lies in understanding what hypothesis testing is. Hypothesis testing is a statistical method used in making inferences or predictions about a population based on a sample's data. A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
02

Identifying the Significant Step

The second step in hypothesis testing is selecting an appropriate testing method. Once the problem is identified and the hypothesis is formulated, there must be a decision on the statistical test method that will be used to test the hypothesis. This decision is driven by the type of data and the purpose behind the testing.
03

Factors Considered in Selecting Testing Method

Some of the factors considered when selecting a testing method include the nature of the data, the scale of measurement, the type of hypothesis, whether your sample data fits a normal distribution, sample size, and whether it's a one-sided or two-sided test.

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Most popular questions from this chapter

"Most Like It Hot" is the title of a press release issued by the Pew Research Center (March 18, 2009, www.pewsocialtrends. org). The press release states that "by an overwhelming margin, Americans want to live in a sunny place." This statement is based on data from a nationally representative sample of 2,260 adult Americans. Of those surveyed, 1,288 indicated that they would prefer to live in a hot climate rather than a cold climate. Suppose that you want to determine if there is convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate. a. What hypotheses should be tested in order to answer this question? b. The \(P\) -value for this test is 0.000001 . What conclusion would you reach if \(\alpha=0.01 ?\) For questions \(10.85-10.86,\) answer the following four key questions (introduced in Section 7.2 ) and indicate whether the method that you would consider would be a large-sample hypothesis test for a population proportion.

Many people have misconceptions about how profitable small, consistent investments can be. In a survey of 1,010 randomly selected American adults (Associated Press, October 29,1999 ), only 374 responded that they thought that an investment of \(\$ 25\) per week over 40 years with a \(7 \%\) annual return would result in a sum of over \(\$ 100,000\) (the actual amount would be \(\$ 286,640\) ). Is there convincing evidence that less than \(40 \%\) of U.S. adults think that such an investment would result in a sum of over \(\$ 100,000\) ? Test the relevant hypotheses using \(\alpha=0.05\).

Use the definition of the \(P\) -value to explain the following: a. Why \(H_{0}\) would be rejected if \(P\) -value \(=0.0003\) b. Why \(H_{0}\) would not be rejected if \(P\) -value \(=0.350\)

The article "Breast-Feeding Rates Up Early" (USA Today, Sept. 14,2010 ) summarizes a survey of mothers whose babies were born in \(2009 .\) The Center for Disease Control sets goals for the proportion of mothers who will still be breast-feeding their babies at various ages. The goal for 12 months after birth is 0.25 or more. Suppose that the survey used a random sample of 1,200 mothers and that you want to use the survey data to decide if there is evidence that the goal is not being met. Let \(p\) denote the proportion of all mothers of babies born in 2009 who were still breast-feeding at 12 months. (Hint: See Example 10.10 ) a. Describe the shape, center, and spread of the sampling distribution of \(\hat{p}\) for random samples of size 1,200 if the null hypothesis \(H_{0}: p=0.25\) is true. b. Would you be surprised to observe a sample proportion as small as \(\hat{p}=0.24\) for a sample of size 1,200 if the null hypothesis \(H_{0}: p=0.25\) were true? Explain why or why not. c. Would you be surprised to observe a sample proportion as small as \(\hat{p}=0.20\) for a sample of size 1,200 if the null hypothesis \(H_{0}: p=0.25\) were true? Explain why or why not. d. The actual sample proportion observed in the study was \(\hat{p}=0.22 .\) Based on this sample proportion, is there convincing evidence that the goal is not being met, or is the observed sample proportion consistent with what you would expect to see when the null hypothesis is true? Support your answer with a probability calculation.

In a survey of 1,000 women ages 22 to 35 who work full-time, 540 indicated that they would be willing to give up some personal time in order to make more money (USA Today, March 4, 2010). The sample was selected to be representative of women in the targeted age group. a. Do the sample data provide convincing evidence that a majority of women ages 22 to 35 who work fulltime would be willing to give up some personal time for more money? Test the relevant hypotheses using \(\alpha=0.01\) b. Would it be reasonable to generalize the conclusion from Part (a) to all working women? Explain why or why not.
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