Download Math109 Test3 W12

North Seattle Community College
Winter 2012
ELEMENTARY STATISTICS
2617 MATH 109 - Section 05,
Chapter 5 and 6 - Test 3
STUDENT NAME: __________________________
21st February 2012
QUIZ SCORE: ______________________________
Question 1:
a. The distribution of cholesterol levels in teenage boys is approximately normal
with μ = 170 and σ = 30. Levels above 200 warrant attention. What percent of
teenage boys have levels between 170 and 225?
b. An airline knows from experience that the distribution of the number of suitcases
that get lost each week on a certain route is approximately normal with μ = 15.5
and σ = 3.6. In one year, how many weeks would you expect the airline to lose
between 10 and 20 suitcases?
c. Assume that blood pressure readings are normally distributed with μ = 120 and σ
= 8. A blood pressure reading of 145 or more may require medical attention.
What percent of people have a blood pressure reading greater than 145?
Questions 2:
a. What happens to the mean and standard deviation of the distribution of sample
means as the size of the sample decreases?
I.
The mean of the sample means stays constant and the standard error
increases.
II.
The mean of the sample means stays constant and the standard error
decreases.
III.
The mean of the sample means decreases and the standard error
increases.
IV.
The mean of the sample means increases and the standard error stays
constant.
b. If the sample size is multiplied by 4, what happens to the standard deviation of
the distribution of sample means?
I.
The standard error is halved.
II.
The standard error is decreased by a factor of 4.
III.
The standard error is doubled.
IV.
The standard error is increased by a factor of 4.
Question 3:
a. A nurse at a local hospital is interested in estimating the birth weight of infants.
How large a sample must she select if she desires to be 99% confident that the
true mean is within 2 ounces of the sample mean? The standard deviation of the
birth weights is known to be 7 ounces.
b. In order to set rates, an insurance company is trying to estimate the number of
sick days that full time workers at an auto repair shop take per year. A previous
study indicated that the standard deviation was 2.8 days.
1. How large a sample must be selected if the company wants to be 90%
confident that the true mean differs from the sample mean by no more
than 1 day?
2. Repeat part (a) using a 95% confidence interval.
3. Which level of confidence requires a larger sample size? Explain.
Questions 4
a. A survey of 300 fatal accidents showed that 123 were alcohol related. Construct a
98% confidence interval for the proportion of fatal accidents that were alcohol
related.
b. A survey of 280 homeless persons showed that 63 were veterans. Construct a
90% confidence interval for the proportion of homeless persons who are
veterans.
c. A pollster wishes to estimate the proportion of United States voters who favor
capital punishment. How large a sample is needed in order to be 95% confident
that the sample proportion will not differ from the true proportion by more than
5%?