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Chapter 8: Q. 38 (page 496)
Teens" online profiles Describe a possible source of error that is not included in the margin of error for the confidence interval in Exercise 36
There are possible sources of errors.
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Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of randomly selected mothers during three months of breastfeeding. The mean change in BMC was and the standard deviation was .
(a) Construct and interpret a confidence interval to estimate the mean percent change in BMC in the population.
(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone mineral? Explain.
Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About % of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.
(a) How large a sample must you test to estimate the proportion of PTC tasters within with % con铿乨ence? Answer this question using the % estimate as to the guessed value for .
(b) Answer the question in part (a) again, but this time use the conservative guess . By how much do the two sample sizes differ?
Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems." The researchers defined "frequent binge drinking" as having five or more drinks in row three or more times in the past two weeks. According to this definition, students were classified as frequent binge drinkers.
1. Identify the population and the parameter of interest.
2. Check conditions for constructing a confidence interval for the parameter.
3. Find the critical value for a 99 \% confidence interval. Show your method. Then calculate the interval.
4. Interpret the interval in context.
In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.
1. An AP Statistics class at a large high school conducts a survey. They ask the first students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."
2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.
A radio talk show host with a large audience is interested in the proportion of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the people who phoned in, answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?
I. The data are a random sample from the population of interest.
II. is so large that both are at least .
III. The population is at least times as large as the sample.
(a) I only
(c) III only
(c) I, II, and III
(b) II only
(d) I and II only
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