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Chapter 8: Q 37. (page 522)
More online sales Refer to Exercise 35. Calculate and interpret the standard error of for these data.
The value of standard error is.
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More weight loss Refer to Exercise . Interpret the confidence level.
One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that
a. can be used only for large samples.
b. requires that you know the population standard deviation .
c. requires that you can regard your data as an SRS from the population.
d. requires that the sample size is less than of the population size.
e. a critical value will lead to a wider interval than a critical value.
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.
Losing weight Refer to Exercise 6.
a. Explain what would happen to the length of the interval if the confidence level was decreased to .
b. How would a confidence interval based on triple the sample size compare to the original interval?
c. As Gallup indicates, the percentage point margin of error for this poll includes only sampling variability (what they call 鈥渟ampling error鈥�). What other potential sources of error (Gallup calls these 鈥渘on sampling errors鈥�) could affect the accuracy of the 95% confidence interval?
Bone loss by nursing mothers 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 breast-feeding. 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 of breast-feeding mothers.
b. Based on your interval from part (a), do these data give convincing evidence thatnursing mothers lose bone mineral, on average? Explain your answer.
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