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Chapter 9: Q1CQQ (page 414)

In Exercises 1–5, use the following survey results: Randomly selected subjects were asked if they were aware that the Earth has lost half of its wildlife population during the past 50 years. Among 1121 women, 23% said that they were aware. Among 1084 men, 26% said that they were aware (based on data from a Harris poll).

Biodiversity: Identify the null and alternative hypotheses resulting from the claim that for the people who were aware of the statement, the proportion of women is equal to the proportion of men.

Short Answer

Expert verified

Null hypothesis: The proportion of women who were aware of the factthat the Earth has lost half of its wildlife population during the past 50 years is equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

\({H_0}:{p_1} = {p_2}\)

Alternate Hypothesis: The proportion of women who were about the factthat the Earth has lost half of its wildlife population during the past 50 years is not equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

\({H_1}:{p_1} \ne {\rm{ }}{p_2}\)

Step by step solution

01

Given information

In a sample of 1121 women, 23% said that they were aware of the fact that the Earth has lost half of its wildlife population during the past 50 years. In another sample of 1084 men, 26% said that they were aware that the Earth has lost half of its wildlife population during the past 50 years.

02

Describe the hypotheses

It is claimed that the proportion of women who were aware of the factthat the Earth has lost half of its wildlife population during the past 50 years is equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

The following hypotheses are set up:

Null hypothesis:The proportion of women who were about the factthat the Earth has lost half of its wildlife population during the past 50 years is equal to the proportion of men who were aware of the fact that the Earth has lost half of its wildlife population during the past 50 years.

Symbolically,

\({H_0}:{p_1} = {p_2}\)

Alternate Hypothesis:The proportion of women who were aware of the factthat the Earth has lost half of its wildlife population during the past 50 years was not equal to the proportion of men who were aware that the Earth has lost half of its wildlife population during the past 50 years.

Symbolically,

\({H_1}:{p_1} \ne {\rm{ }}{p_2}\)

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

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a. Use the methods of this section to construct a 95% confidence interval estimate of the difference p1-p2. What does the result suggest about the equality of p1andp2?

b. Use the methods of Section 7-1 to construct individual 95% confidence interval estimates for each of the two population proportions. After comparing the overlap between the two confidence intervals, what do you conclude about the equality ofp1andp2?

c. Use a 0.05 significance level to test the claim that the two population proportions are equal. What do you conclude?

d. Based on the preceding results, what should you conclude about the equality ofp1andp2? Which of the three preceding methods is least effective in testing for the equality ofp1andp2?

Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

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a. Test the claim using a hypothesis test.

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Is Echinacea Effective for Colds? Rhinoviruses typically cause common colds. In a test of the effectiveness of Echinacea, 40 of the 45 subjects treated with Echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). We want to use a 0.05 significance level to test the claim that Echinacea has an effect on rhinovirus infections.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. Based on the results, does Echinacea appear to have any effect on the infection rate?

esting Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Accuracy of Fast Food Drive-Through Orders In a study of Burger King drive-through orders, it was found that 264 orders were accurate and 54 were not accurate. For McDonald’s, 329 orders were found to be accurate while 33 orders were not accurate (based on data from QSR magazine). Use a 0.05 significance level to test the claim that Burger King and McDonald’s have the same accuracy rates.

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Hypothesis Tests and Confidence Intervals for Hemoglobin

a. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean hemoglobin levels, will the hypothesis tests and the confidence interval result in the same conclusion?

b. In general, if you conduct a hypothesis test using the methods of Part 1 of this section, will the P-value method, the critical value method, and the confidence interval method result in the same conclusion?

c. Assume that you want to use a 0.01 significance level to test the claim that the mean haemoglobin level in women is lessthan the mean hemoglobin level in men. What confidence level should be used if you want to test that claim using a confidence interval?
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