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Chapter 9: Q5CQQ (page 414)

In Exercises 1鈥�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 Assume that a P-value of 0.1 is obtained when testing the claim given in Exercise 1 鈥淏iodiversity.鈥� What should be concluded about the null hypothesis? What should be the final conclusion?

Short Answer

Expert verified

The null hypothesis fails to be rejected.

There is insufficient evidence to reject the claim that the proportion of women who were aware of the fact is equal to the proportion of men who were aware of the fact.

Step by step solution

01

Step 1: 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 1048 men, 26% said that they were aware that the Earth has lost half of its wildlife population during the past 50 years.

It is claimed that the proportion of women who were about the fact is equal to the proportion of men who were aware of the fact.

02

Formulation of the hypotheses

Null hypothesis: The proportion of women who were aware of the factis equal to the proportion of men who were aware of the fact.

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

Alternative hypothesis:The proportion of women who were aware of the factis not equal to the proportion of men who were aware of the fact.

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

03

Interpretation of the p-value

The p-value is equal to 0.1.

Let the level of significance be equal to 0.05.

Since the p-value is greater than 0.05, the null hypothesis fails to be rejected.

There is insufficient evidence to reject the claimthat the proportion of women who were aware of the factis equal to the proportion of men who were aware of the fact.

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Most popular questions from this chapter

In Exercises 5鈥�20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of 鈥渄ebilitating test anxiety,鈥� which most of us call panic or blanking out (based on data from 鈥淚tem Arrangement, Cognitive Entry Characteristics, Sex and Test Anxiety as Predictors of Achievement in Examination Performance,鈥� by Klimko, Journal of Experimental Education, Vol. 52, No. 4.) Is there sufficient evidence to support the claim that the two populations of scores have different means? Is there sufficient evidence to support the claim that the arrangement of the test items has an effect on the score? Is the conclusion affected by whether the significance level is 0.05 or 0.01?

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In Exercises 5鈥�20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)

Seat Belts A study of seat belt use involved children who were hospitalized after motor vehicle crashes. For a group of 123 children who were wearing seat belts, the number of days in intensive care units (ICU) has a mean of 0.83 and a standard deviation of 1.77. For a group of 290 children who were not wearing seat belts, the number of days spent in ICUs has a mean of 1.39 and a standard deviation of 3.06 (based on data from 鈥淢orbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts,鈥� by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No. 3).

a. Use a 0.05 significance level to test the claim that children wearing seat belts have a lower mean length of time in an ICU than the mean for children not wearing seat belts.

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

c. What important conclusion do the results suggest?

Confidence Interval for Haemoglobin

Large samples of women and men are obtained, and the haemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:\(\)\( - 1.76g/dL < {\mu _1} - {\mu _2} < - 1.62g/dL\).

a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?

b. Write a brief statement that interprets that confidence interval.

c. Express the confidence interval with measures from men being population 1 and measures from women being population 2.

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\))

Regular Coke and Diet Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includesweights (lb) of the contents of cans of Diet Coke (n= 36,\(\overline x \)= 0.78479 lb, s= 0.00439 lb) and of the contents of cans of regular Coke (n= 36,\(\overline x \)= 0.81682 lb, s= 0.00751 lb).

a. Use a 0.05 significance level to test the claim that the contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke.

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. Can you explain why cans of Diet Coke would weigh less than cans of regular Coke?

Verifying requirements in the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group considered of 201,229 children given the sulk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the sulk vaccine, are the requirements for a hypothesis test satisfied? Explain.
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