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Chapter 8: Q 38. (page 522)
More cheating Refer to Exercise 36. Calculate and interpret the standard error of for these data.
The value of standard error is.
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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.
Bottling cola A particular type of diet cola advertises that each can contains ounces of the beverage. Each hour, a supervisor selects cans at random, measures their contents, and computes a confidence interval for the true mean volume. For one particular hour, the confidence interval is ounces to ounces.
a. Does the confidence interval provide convincing evidence that the true mean volume is different than ounces? Explain your answer.
b. Does the confidence interval provide convincing evidence that the true mean volume is ounces? Explain your answer.
Engine parts A random sample of 16 of the more than auto engine crankshafts produced in one day was selected. Here are measurements (in millimeters) of a critical component on these crankshafts:
a. Construct and interpret a confidence interval for the mean length of this component on all the crankshafts produced on that day.
b. The mean length is supposed to be mm but can drift away from this target during production. Does your interval from part (a) suggest that the mean has drifted from mm? Explain your answer.
Employment in CaliforniaEach month the government releases unemployment
statistics. The stated unemployment rate doesn鈥檛 include people who choose not to be employed, such as retirees. Based on a random sample of California adults, a confidence interval for the proportion of all California adults employed in the workforce is
a. Interpret the confidence level.
b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?
c. Describe how untruthful answers might lead to bias in this survey. Does the stated margin of error account for this possible bias?
The student body president of a high school claims to know the names of at least of the 1800 students who attend the school. To test this claim, the student government advisor randomly selects students and asks the president to identify each by name. The president successfully names only of the students.
a. Identify the population and parameter of interest.
b. Check conditions for constructing a confidence interval for the parameter.
c. Construct a confidence interval for p.
d. Interpret the interval in context.
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