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Chapter 10: Q 13. (page 640)

Ban junk food! A CBS News poll asked 606 randomly selected women and 442

randomly selected men, 鈥淒o you think putting a special tax on junk food would encourage more people to lose weight?鈥� 170 of the women and 102 of the men said 鈥淵es.鈥� A 99% confidence interval for the difference (Women 鈥� Men) in the true proportion of people in each population who would say 鈥淵es鈥� is 鈭�0.020to0.120. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

Short Answer

Expert verified

It provides convincing evidence that two population proportions are equal.

Step by step solution

01

Given Information

It is given that at99%confidence interval, we got(-0.020,0.120).

02

Explanation

The given confidence interval has zero in it. Hence, it is likely that difference in proportion is zero and two population proportions are equal.

So, it is possible that population proportions are equal. Therefore, there is no convincing evidence that two population proportions are not equal.

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Most popular questions from this chapter

鈥淚 can鈥檛 get through my day without coffee鈥� is a common statement from many college students. They assume that the benefits of coffee include staying awake during lectures and remaining more alert during exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee 1 hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee 1 hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup).

a. One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday鈥檚 test and one cup of coffee before Wednesday鈥檚 test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

b. The researchers actually used the better method of deciding when each subject receives the two treatments that you identified in part (a). For each subject, the number of words recalled when drinking no coffee and when drinking one cup of coffee is recorded in the table. Carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory, on average, for students like the ones in this study.

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is 0.45. In a simple random sample of 250people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. 0.4975

b. 0.2475

c. 0.0315

d. 0.0009

e.0

The following dot plots show the average high temperatures (in degrees Celsius) for a sample of tourist cities from around the world. Both the January and July average high temperatures are shown. What is one statement that can be made with certainty from an Page Number: 704 analysis of the graphical display?

a. Every city has a larger average high temperature in July than in January.

b. The distribution of temperatures in July is skewed right, while the distribution of temperatures in January is skewed left.

c. The median average high temperature for January is higher than the median average high temperature for July.

d. There appear to be outliers in the average high temperatures for January and July.

e. There is more variability in average high temperatures in January than in July

You can find some interesting polls online. Anyone can become part of the sample just by clicking on a response. One such poll asked, 鈥淒o you prefer watching first-run movies at a movie theater, or waiting until they are available to watch at home or on a digital device?鈥� In all, 8896people responded, with only 12%(1118people) saying they preferred theaters. You can conclude that

a. American adults strongly prefer watching movies at home or on their digital devices.

b. the high nonresponse rate prevents us from drawing a conclusion.

c. the sample is too small to draw any conclusion.

d. the poll uses voluntary response, so the results tell us little about all American adults.

e. American adults strongly prefer seeing movies at a movie theater.

A quiz question gives random samples of n=10observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9degrees of freedom to calculate a 95%confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample t Interval with 16.87degrees of freedom to compute the 95%confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

(a) Tom's confidence interval is wider.

(b) Janelle's confidence Interval is wider.

(c) Both confidence Intervals are the same.

(d) There is insufficient information to determine which confidence interval is wider.

(e) Janelle made a mistake, degrees of freedom has to be a whole number.
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