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Chapter 10: Q 14. (page 640)

Artificial trees? An association of Christmas tree growers in Indiana wants to know if there is a difference in preference for natural trees between urban and rural households. So the association sponsored a survey of Indiana households that had a Christmas tree last year to find out. In a random sample of 160rural households, 64had a natural tree. In a separate random sample of 261urban households, 89had a natural tree. A 95%confidence interval for the difference (Rural 鈥� Urban) in the true proportion of households in each population that had a natural tree is -0.036to0.154. 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 proportion are equal.

Step by step solution

01

Given Information

It is given that we have(-0.036,0.154)at95%confidence interval.

02

Explanation

The interval (-0.036,0.154)contains zero, It is likely that difference of proportion is zero. Two population proportions can be equal.

It implies that there is possibility that population proportions are equal.

It can be concluded that there is no convincing evidence that two population proportions are not equal.

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Most popular questions from this chapter

Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of H0:渭T鈭�渭P=0versus Ha:渭T鈭�渭P>0, where 渭T= the true mean reduction in blood pressure when taking the natural product and 渭P = the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like to detect whether the natural product reduces blood pressure by at least 7points more, on average, than the placebo. If groups of size 50are used in the experiment, a twosample t test using 伪=0.01will have a power of 80%to detect a 7-point difference in mean blood pressure reduction. If the researchers want to be able to detect a 5-point difference instead, then the power of the test

a. would be less than 80%.

b. would be greater than 80%.

c. would still be 80%.

d. could be either less than or greater than 80%.

e. would vary depending on the standard deviation of the data

Bird eggs A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of the small nests and the other of large nests. Then she weighs one egg (chosen at random if there is more than one egg) from each nest. A 95% confidence interval for the difference (Large 鈭� Small) between the mean mass (in

grams) of eggs in small and large nests is 1.6卤2.0 role="math" localid="1654714720708" 3051526=0.200=20.0%1.6卤2.0

a. Does the interval provide convincing evidence of a difference in the true mean egg mass of birds with small nests and birds with large nests? Explain your answer.

b. Does the interval provide convincing evidence that the true mean egg mass of birds with small nests and birds with large nests is the same? Explain your answer.

Digital video disks A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select 500DVDs produced by each fabricator and find that 484of the disks produced by the first machine are acceptable and 480of the disks produced by the second machine are acceptable. If p1,p2are the proportions of acceptable DVDs produced by the first and second machines, respectively, check if the conditions for calculating a confidence interval for p1-p2are met.

Researchers wondered whether maintaining a patient鈥檚 body temperature close to normal by heating the patient during surgery would affect rates of infection of wounds. Patients were assigned at random to two groups: the normothermic group (core temperatures were maintained at near normal, 36.5掳C, using heating blankets) and the hypothermic group (core temperatures were allowed to decrease to about 34.5掳C). If keeping patients warm during surgery alters the chance of infection, patients in the two groups should show a difference in the average length of their hospital stays. Here are summary statistics on hospital stay (in number of days) for the two groups:

a. Construct and interpret a 95%confidence interval for the difference in the true mean length of hospital stay for normothermic and hypothermic patients like these.

b. Does your interval in part (a) suggest that keeping patients warm during surgery affects the average length of patients鈥� hospital stays? Justify your answer.

c. Interpret the meaning of 鈥�95%confidence鈥� in the context of this study.

A random sample of size n will be selected from a population, and the proportion p^3051526=0.200=20.0%p^ of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95% confidence interval be affected if the sample size were increased from 50to200 and the sample proportion of people who have a Facebook page is unchanged?

a. It remains the same.

b. It is multiplied by 2.

c. It is multiplied by 4.

d. It is divided by 2.

e. It is divided by 4.
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