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Chapter 8: Q.46 (page 479)
Which distribution should you use for this problem?
The distribution required for this problem is distribution with parameters
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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?
Fill in the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample mean.
A sample of small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of ounces. The population standard deviation is known to be ounce.
a.
b. In words, define the random variable .
c. In words, define the random variable .
d. Which distribution should you use for this problem? Explain your choice.
e. Construct a confidence interval for the population mean weight of the candies.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
f. Construct a confidence interval for the population mean weight of the candies.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
g. In complete sentences, explain why the confidence interval in part is larger than the confidence interval in part .
h. In complete sentences, give an interpretation of what the interval in part means.
Suppose that an accounting firm does a study to determine the time needed to complete one person鈥檚 tax forms. It
randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The
population distribution is assumed to be normal.
a. I. =________
ii. 蟽 =________
iii. n =________
b. In words, define the random variables X and
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a 90% confidence interval for the population mean time to complete the tax forms.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey,
what changes should it make?
f. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to
the level of confidence? Why?
g. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to
within one hour. How would the number of people the firm surveys change? Why?
Explain in complete sentences what the confidence interval means.
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