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Chapter 8: Q.12 (page 477)
Suppose the Census needed to be confident of the population mean length of time. Would the Census have to survey more people? Why or why not?
It is not required for the census to survey a larger number of people because the level of confidence does not depend on the sample size.
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The population standard deviation for the height of high school basketball players is three inches. If we want to be % confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?
The data in Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag.
Construct a 95% confidence interval for the true mean number of colors on national flags.
Using the same , , and n = 39, how would the error bound change if the confidence level were reduced to 90%? Why?
How much area is in both tails (combined)?
A random survey of enrollment at 35 community colleges across the United States yielded the following figures:
6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044; 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000;
9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080;
11,622. Assume the underlying population is normal.
a. i. = __________
ii. sx = __________
iii. n = __________
iv. n 鈥� 1 = __________
b. Define the random variables X and in words.
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United
States.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?
Forbes magazine published data on the best small firms in . These were firms that had been publicly traded for at least a year, have a stock price of at least per share, and have reported annual revenue between million and billion.
The Table 8.13 shows the ages of the corporate CEOs for a random sample of these firms.
Use this sample data to construct a confidence interval for the mean age of CEO鈥檚 for these top small firms. Use the Student's t-distribution.
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