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Chapter 8: Q. 29 (page 522)
Latoya wants to estimate the proportion of the seniors at her boarding school who like the cafeteria food. She interviews an SRS of of the seniors and finds that think the cafeteria food is good.
The sample size condition does not meet.
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Running red lights A random digit dialing telephone survey of 880 drivers asked, 鈥淩ecalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?鈥� Of the 880 respondents, 171 admitted that at least one light had been red.37
a. Construct and interpret a 95% confidence interval for the population proportion.
b. Nonresponse is a practical problem for this survey鈥攐nly 21.6% of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why? Are these sources of bias included in the margin of error?
Student body totals Use your interval from Exercise 40 to construct and interpret a confidence interval for the total number of students at the school that the student body president can identify by name. Then use your interval to evaluate the president鈥檚 claim.
In a poll conducted by phone,
I. Some people refused to answer questions.
II. People without telephones could not be in the sample.
III. Some people never answered the phone in several calls.
Which of these possible sources of bias is included in the margin of error announced for the poll?
a. I only
b. II only
c. III only
d. I, II, and III
e. None of these
Willows in Yellowstone Writers in some fields summarize data by giving x 虅 and its
standard error rather than .Biologists studying willow plants in Yellowstone National Park reported their results in a table with columns labeled The table entry for the heights of willow plants (in centimeters) in one region of the park was . The researchers measured a total of plants.
a. Find the sample standard deviation for these measurements.
b. A hasty reader believes that the interval given in the table is a confidence interval for the mean height of willow plants in this region of the park. Find the actual confidence level for the given interval.
t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.
a. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population means?
b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.
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