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Chapter 8: Q.36 (page 479)
Using the same mean, standard deviation, and level of confidence, suppose that n were 69 instead of 25. Would the error bound become larger or smaller? How do you know?
The error bound will become smaller.
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Suppose we know that a confidence interval is (). Find the error bound and the sample mean.
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats.
a. i. __________
ii. __________
iii. __________
iv. __________
b. Define the random variables and in words.
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a 92% confidence interval for the population mean number of unoccupied seats per flight.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
Why would the error bound change if the confidence level were lowered to?
In a recent sample of used car sales costs, the sample mean was with a standard deviation of . Assume
the underlying distribution is approximately normal.
a. Which distribution should you use for this problem? Explain your choice.
b. Define the random variablein words.
c. Construct a confidence interval for the population mean cost of a used car.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
d. Explain what a 鈥� confidence interval鈥� means for this study.
Suppose that the insurance companies did do a survey. They randomly surveyed drivers and found that claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.
a. i. x = __________ ii. n = __________ iii. p鈥� = __________
b. Define the random variables and , in words.
c. Which distribution should you use for this problem? Explain your choice.
d. Construct a confidence interval for the population proportion who claim they always buckle up. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound.
e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.
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