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Fall 2009 Math 227 Test #3
Name: _____________________________
For confidence interval, you need to find the critical value and the margin of error. For hypothesis
testing, you need to show all the steps. Total Points: 80
1.
The tobacco industry closely monitors all surveys that involve smoking. One survey showed that
among 800 randomly selected subjects who completed four years of college, 18.5% smoke.
Construct a 99% confidence interval for the true percentage of smokers among all people who
completed four years of college.
Critical value: ____________
(8)
Margin of Error: ____________
Confidence Interval: ______________
2.
(10)A
light-bulb manufacturer advertises that the average life for its energy saving light bulbs is 900
hours. A random sample of 15 of its energy saving light bulbs resulted in the following lives in hours.
995 590 510 539 739 917 571 555
916 728 664 693 708 887 849
Assuming that the population is normally distributed, at a 10% level of significance; test the claim
that the mean life for the company's light bulbs is less than that from the advertised mean? Use the P–
value method.
Sample size: _________Sample Mean: __________ Sample Standard Deviation_____________
Hypothesis Testing: (Show all steps)
3.
(6)The
department of Mathematics at a four-year university wants to estimate the average age of
students who apply to their graduate program with 98% confidence level. If the standard
deviation of the ages is known to be 10 years of age with a margin of error of 2 years, how large
must the sample be?
4.
(8)A
savings and loan bank needs information concerning the checking account balances of its local
customers. A random sample of 46 accounts were researched and yielded a mean balance of $664.14
and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking
account balance for local customers.
Critical Value: _____________
Margin of Error: ____________
Confidence Interval: __________________
5.
(6)A
Statistics major attending UCLA wants to take a survey of families who like Math. He wants to
be 96% sure that the true proportion of families who like Math is no more than 1.5% of the true
proportion. Compute the sample size if she has some idea of past research about the estimate of this
proportion and that is 25%.
6.
(10) A
machine dispenses a liquid into bottles in such a way that the standard deviation of the contents
is 81 milliliters and the population is normally distributed. A new machine is tested on a sample of 24
containers and the standard deviation for this sample group is found to be 85 milliliters. At the 0.05
level of significance, test the claim that the amounts dispensed by the new machine have a greater
standard deviation.
7.
(10)A
poll of 1,068 adult Americans reveals that 513 of the voters surveyed prefer the Democratic
candidate for the presidency. Test the claim that 50% of all voters prefer the Democratic candidate
for the presidency. Use   0.01
8.
(11)A
sample of 15 one-pound jars of coffee of Brand I showed that the mean amount of caffeine in
these jars is 80 milligrams per jar with a standard deviation of 5 milligrams. Another sample of 12
one-pound coffee jars of Brand II gave a mean amount of caffeine equal to 77 milligrams per jar with
a standard deviation of 6 milligrams. Construct a confidence interval for the difference between the
mean amounts of caffeine in one-pound coffee jars of these two brands. Assume that the two
populations are normally distributed wand the standard deviations of the two populations are not
equal.
Critical Value: _______________
Margin of Error: __________________
Confidence Interval: ___________________
9.
(11)According
to a study, the percentage of companies that hosted holiday parties was 57% in 2007
and 54% in 2008. Suppose that this study is based on samples of 1000 and 1200 companies for 2007
and 2008, respectively. Test whether the percentages of companies that hosted holiday parties in
2007 and 2008 are different. Use 1% significance level.