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Chapter 8: Q.48 (page 480)
Why would the error bound change if the confidence level were lowered to?
The error bound will become smaller if the confidence level were lowered to,
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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.
Define the random variable in words.
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?
You do a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each night. You measure hours of sleep for subjects with the following results. Construct a % confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data. ; ; ; ; ; ; ; ; ; ; ;
Suppose that children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had
to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of
three months. Assume that the underlying population distribution is normal.
b. Define the random variable in words.
c. Define the random variable in words.
d. Which distribution should you use for this problem? Explain your choice.
e. Construct a confidence interval for the population mean length of time using training wheels.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
f. Why would the error bound change if the confidence level were lowered to ?
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