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CareerBuilder.com conducted a survey to learn about the proportion of employers who perform background checks when evaluating a candidate for employment ("Majority of Employers Background Check Employees...Here's Why," November \(17,\) \(2016,\) retrieved November 19,2016 ). Suppose you are interested in determining if the resulting data provide strong evidence in support of the claim that more than two-thirds of employers perform background checks. To answer this question, what null and alternative hypotheses should you test? (Hint: See Example \(10.4 .)\)

In a hypothesis test, what does it mean to say that the null hypothesis was rejected?

The article "Public Acceptability in the UK and the USA of Nudging to Reduce Obesity: The Example of Reducing Sugar-Sweetened Beverages" (PLOS One, June 8,2016 ) describes a survey in which each person in a representative sample of 1082 adult Americans was asked about whether they would find different types of interventions acceptable in an effort to reduce consumption of sugary beverages. When asked about a tax on sugary beverages, 459 of the people in the sample said they thought that this would be an acceptable intervention. These data were used to test \(H_{0}: p=0.5\) versus \(H_{a^{*}}: p<0.5\) and the null hypothesis was rejected. a. Based on the hypothesis test, what can you conclude about the proportion of adult Americans who think that taxing sugary beverages is an acceptable intervention in an effort to reduce consumption of sugary beverages? b. Is it reasonable to say that the data provide strong support for the alternative hypothesis? c. Is it reasonable to say that the data provide strong evidence against the null hypothesis?

In a hypothesis test, what does it mean to say that the null hypothesis was not rejected?

One type of error in a hypothesis test is rejecting the null hypothesis when it is true. What is the other type of error that might occur when a hypothesis test is carried out?

Suppose that for a particular hypothesis test, the consequences of a Type I error are very serious. Would you want to carry out the test using a small significance level \(\alpha\) (such as 0.01 ) or a larger significance level (such as 0.10 )? Explain the reason for your choice.

Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite. A consumer group wants to investigate a claim that the proportion of defective flares made by a particular manufacturer is higher than the advertised value of \(0.10 .\) A large number of flares will be tested, and the results will be used to decide between \(H_{0}: p=0.10\) and \(H_{a}: p>0.10,\) where \(p\) represents the actual proportion of defective flares made by this manufacturer. If \(H_{0}\) is rejected, charges of false advertising will be filed against the manufacturer. a. Explain why the alternative hypothesis was chosen to be \(H: p>0.10 .\) b. Complete the last two columns of the following table. (Hint: See Example 10.7 for an example of how this is done.)

A television manufacturer states that at least \(90 \%\) of its TV sets will not need service during the first 3 years of operation. A consumer group wants to investigate this statement. A random sample of \(n=100\) purchasers is selected and each person is asked if the set purchased needed repair during the first 3 years. Let \(p\) denote the proportion of all sets made by this manufacturer that will not need service in the first 3 years. The consumer group does not want to claim false advertising unless there is strong evidence that \(p<0.90\). The appropriate hypotheses are then \(H_{0}: p=0.90\) versus \(H_{a}: p<0.90\). a. In the context of this problem, describe Type I and Type II errors, and discuss the possible consequences of each. b. Would you recommend a test procedure that uses \(\alpha=\) 0.01 or one that uses \(\alpha=0.10 ?\) Explain. (Hint: See Example \(10.9 .)\)

One type of error in a hypothesis test is failing to reject a false null hypothesis. What is the other type of error that might occur when a hypothesis test is carried out?

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is expensive, so it will be done only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers. Let \(p\) denote the actual proportion of defective installations for the robots. It is known that the proportion of defective installations for human assemblers is 0.02 . a. Which of the following pairs of hypotheses should the manufacturer test? $$ H_{0}: p=0.02 \text { versus } H_{a}: p<0.02 $$ or $$ H_{0}: p=0.02 \text { versus } H_{a}: p>0.02 $$ Explain your choice. b. In the context of this exercise, describe Type 1 and Type II errors. c. Would you prefer a test with \(\alpha=0.01\) or \(\alpha=0.10 ?\) Explain your reasoning.