& Answers with rationales (Chapter 1-12)
The mean number of travel days per year for salespeople
employed by three hardware distributors needs to be
estimated with a 0.90 degree of confidence. For a small
pilot study, the mean was 150 days and the standard
deviation was 14 days. If the population mean is estimated
within two days, how many salespeople should be
sampled? - -ANSWER--133
A research firm needs to estimate within 3% the proportion
of junior executives leaving large manufacturing
companies within three years. A 0.95 degree of
confidence is to be used. Several years ago, a study
revealed that 21% of junior executives left their company
within three years. To update this study, how many junior
executives should be surveyed? - -ANSWER--709
There are 2,000 eligible voters in a precinct. A total of 500
voters are randomly selected and asked whether they plan
to vote for the Democratic incumbent or the Republican
challenger. Of the 500 surveyed, 350 said they would vote
for the Democratic incumbent. Using the 0.99 confidence
, coefficient, what are the confidence limits for the
proportion that plan to vote for the Democratic incumbent?
- -ANSWER--0.647 and 0.753
A random sample of 85 supervisors revealed that they
worked an average of 6.5 years before being promoted.
The population standard deviation was 1.7 years. Using
the 0.95 degree of confidence, what is the confidence
interval for the population mean? - -ANSWER--6.14 and
6.86
The mean weight of trucks traveling on a particular section
of I-475 is not known. A state highway inspector needs an
estimate of the population mean. He selects and weighs a
random sample of 49 trucks and finds the mean weight is
15.8 tons. The population standard deviation is 3.8 tons.
What is the 95% confidence interval for the population
mean? - -ANSWER--14.7 and 16.9
A bank wishes to estimate the mean credit card balance
owed by its customers. The population standard deviation
is estimated to be $300. If a 98% confidence interval is
used and an interval of $75 is desired, how many
customers should be sampled? - -ANSWER--87
A group of statistics students decided to conduct a survey
at their university to find the average (mean) amount of
time students spent studying per week. Assuming a
population standard deviation of three hours, what is the
required sample size if the error should be less than a half
hour with a 99% level of confidence? - -ANSWER--239