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Large Sample Confidence Interval
An increase in the rate of consumer savings is
frequently tied to a lack of confidence in the
economy and is said to be an indicator of a
recessional tendency in the economy. A random
sampling of n = 200 savings accounts in a local
community showed a mean increase in savings
account values of 7.2% over the past 12 months
and a standard deviation of 5.6%. Estimate the
mean percentage increase in savings account
values over the past 12 months for depositors in
the community. Place a bound on your error of
estimation.
Small Sample Confidence Interval
Varying costs, primarily labor, make home building vary from
one unit to the next. A builder of standard tract homes
needs to make an average profit in excess of $8500 per
home in order to achieve an annual profit goal. The profits
per home for the builder's most recent five units are $8760,
$6370, $9620, $8200, and $10,350.
A) Find a 95% confidence interval for the builder's mean
profit per unit. Interpret this interval
B) Does the interval constructed in part (A) contain
$8500? Would you conclude that the builder is operating at
the desired profit level?
Confidence Interval for Proportions
An article titled "Dreaded Tourists Pretty Well Liked in Vermont,
Poll Shows" reports on a poll of 504 Vermonters conducted by
the University of Vermont and the State Department of Forests,
Parks, and Recreation (New York times, July 6, 1986). The
random sample, contacted by telephone, answered more than a
hundred questions about the respondents' attitudes toward
tourists and the impact of tourism on wildlife, recreation, and
other factors that affect the quality of life in the state. The
survey found, for example, that 63% said tourists were wealthy
and 70% said tourists had a good sense of humor. Half believed
that tourism would raise the standard of living in Vermont. How
accurate are these estimates of the corresponding population
percentages? Give an approximate bound on the error of
estimation.
Bounds on Proportions
In earlier exercises we described the results of a government
survey of telephone use by federal employees; particularly,
we noted that approximately one in three calls is made for
personal (i.e., nonbusiness) reasons (New York Times, June
23, 1986). The government did not listen in on employee's
calls to determine whether an employee's phone call was
for business or personal reasons. Rather, it randomly
sampled the number dialed and checked the source of each
number. Suppose that the government wanted to estimate
the proportion of nonbusiness calls made by its employees
correct to within .02 with probability equal to .99.
Approximately how many dialed telephone numbers would
have to be included in the sample?