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Chapter 8: Problem 57

When a person stands trial for murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null hypothesis, or is it an example of an alternative hypothesis?

Short Answer

Expert verified
The claim of innocence in a trial corresponds to the null hypothesis in a statistical test.

Step by step solution

01

Understanding the scenario

In a trial, the jury is instructed to assume that the defendant is innocent. This assumption is established before any evidence has been reviewed.
02

Identify the null hypothesis

In the context of hypothesis testing in statistics, the null hypothesis is generally a claim of no effect or no difference. It's the default assumption that we start with before reviewing any evidence.
03

Interpret the scenario in the context of hypothesis testing

Referring back to the court case, the assumption of innocence can be seen as the default position before any evidence is presented, similar to a null hypothesis in a statistical test. Therefore, the claim of innocence can be identified as a null hypothesis.
04

Identify the alternative hypothesis

In contrast, if the defendant was assumed to be guilty, this would be the alternative hypothesis. It鈥檚 what we would test the null hypothesis (assumption of innocence) against after reviewing the evidence.

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Most popular questions from this chapter

A poll in California (done by the Public Policy Institute) asked whether the government should regulate greenhouse gases, and 751 out of 1138 likely voters said yes. However, when a different polling agency asked whether stricter environmental controls are worth the cost, 523 of 1138 likely voters said yes; the alternative was that the laws hurt the economy and cost too many jobs. (Source: Ventura County Star, March 21,2013 ) a. Find both sample proportions and compare them. Comment on the similarities of the two questions. b. Determine whether the two sample proportions are significantly different at a \(0.05\) significance level. Comment on the effect of changing the wording of this question. c. Using methods learned in Chapter 7 , find a \(95 \%\) confidence interval for the difference between the two percentages, and interpret it. Does it capture \(0 ?\) What does that mean?

Choose one of the answers given. The null hypothesis is always a statement about a (sample statistic or population parameter).

An arthritis diet claims that the disease can be relieved by reducing sugar from the diet. To test this claim, a researcher randomly assigns arthritis patients to two groups. Both groups eat the same amount of calories, but one group eats almost no sugar and the other group includes sugar in their meal. After 3 months, the doctor tests the claim that the sugar-free diet is better than the usual diet. She records the proportion of each group that got relieved of almost \(10 \%\) of their problem. She then announced that she failed to reject the null hypothesis. Which of the following are valid interpretations of her findings? a. The sugar-free dict was less effective than the normal diet. b. The researcher did not see enough evidence to conclude that the sugarfree diet was more effective. c. The sugar-free diet and the normal diet were equally effective. d. There were no significant differences in effectiveness between the sugar- free diet and normal diet.

Give the null and alternative hypothesis for each test, and state whether a oneproportion z-test or a two-proportion z-test would be appropriate. a. You test a random sample of eighth-grade students who play daily for 3 hours and devote the same time to homework, comparing boys and girls. b. You test a person to see whether she can tell butter on bread from margarine spread on bread. You give her 20 toast bits selected randomly (half with butter and half with margarine) and record the proportion she gets correct to test the hypothesis.

According to one source, \(50 \%\) of plane crashes are due at least in part to pilot error (http://www.planecrashinfo.com). Suppose that in a random sample of 100 separate airplane accidents, 62 of them were due to pilot error (at least in part.) a. Test the null hypothesis that the proportion of airplane accidents due to pilot error is not \(0.50\). Use a significance level of \(0.05\). b. Choose the correct interpretation: i. The percentage of plane crashes due to pilot error is not significantly different from \(50 \%\). ii. The percentage of plane crashes due to pilot error is significantly different from \(50 \%\).
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