Statistics B
Chapter 7 Practice Test
1. Which of the following is the critical value t 2 that corresponds to a confidence level of 90%
and a sample size of n = 31?
A) 1.697
B) 1.645
C) 1.310
D) not enough information
2. Which of the following is the critical value z 2 that corresponds to a confidence level of 92%?
A) 1.41
B) 1.75
C) 1.96
D) not enough information
3. Which of the following is the margin of error (E) calculated for the 95% confidence interval
used to estimate the population proportion: in a survey of 4100 TV viewers, 20% said they
watch network news programs
A) 0.00915
B) 0.0160
C) 0.0140
D) 0.0122
4. Which of the following is the minimum sample size needed to assure that an estimate of p
will be within 5% at a 95% confidence level? Both pˆ and qˆ are unknown.
A) 384
B) 385
C) 196
D) 197
5. Which of the following is the margin of error calculated from the following: 99% confidence,
n  74 , x  3795 ,   883 ?
A) 1136
B) 264
C) 32
D) 272
6. Which of the following is the margin of error calculated from the following: 95% confidence,
n  21 , x  0.44 , s  0.44 ?
A) 0.17
B) 0.04
C) 0.19
D) 0.20
7. Which of the following is the minimum sample size needed to assure that an estimate of 
will have a margin of error of 126 at a 99% confidence level, with   534 ?
A) 10
B) 11
C) 119
D) 120
8. Which of the following is the critical “  L2 ” value for a sample size of 9 and a confidence level
of 98%?
A) 2.088
B) 1.646
C) 21.666
D) 20.090
9. Write a statement interpreting the confidence interval “ 0.485  p  0.549 ” for a 95%
confidence level.
We are 95% confident that the true value of the population proportion, p, is between 0.485 and 0.549. If many
samples of the same size were taken, 95% of them would contain the true value of p.
10. Before 1964, U.S. quarters were made with 90% silver and 10% copper. Since 1964, they
have been made with a (cheaper) silver-nickel alloy. A sample of each kind of quarter is
shown in Data Set 14 in Appendix B on page 802…you will need to enter the “Pre-1964
Quarters” and the “Post-1964 Quarters” lists into your calculator.
a. Construct a 99% confidence interval for , the mean weight of all “Pre-1964” quarters.
Round interval limits to one more decimal place than the data.
6.19267  0.03764 or 6.15503    6.23031
b. Construct a 99% confidence interval for , the mean weight of all “Post-1964” quarters.
Round interval limits to one more decimal place than the data.
5.63930  0.02652 or 5.61278    5.66582
c. Explain whether it can be concluded from the confidence intervals that changing the
composition of the quarters resulted in quarters that weigh less.
YES – the confidence interval for the “Post-1964” quarters is less than the interval for
“Pre-1964” quarters, with no overlap
11. A random sample of 186 babies has a mean birth weight of x  3103 grams with a sample
standard deviation of 696 grams. Construct the 95% confidence interval for the mean birth
weight, , of all babies. Round interval limits to the nearest whole number
3103  101 or 3002    3204
12. Use your result from the previous problem to explain whether the sample of babies can be
from a population with a known mean birth weight of 3420 grams.
NO, the interval does not contain “3420”, so we are (95%) confident that the true mean
weight is less than 3420.
13. In a laboratory, a random sample of 464 light bulbs were tested, and 424 of those bulbs
lasted more than 500 hours.
a. Calculate the proportion of bulbs that last more than 500 hours. Round to three decimal
places.
pˆ  .914
b. Construct the 99% confidence interval for p, the proportion of all such bulbs that last
more than 500 hours. Round interval limits to three decimal places.
.914  0.034 or 0.880  p  0.948
c. Use your confidence interval to explain whether the light bulb company can honestly
state that “at least 90%” of its bulbs last more than 500 hours.
NO, the confidence interval goes below 90% (0.900), which means it’s very possible that
the true proportion is as low as 88%.
d. Find the minimum sample size needed to ensure that the margin of error is no more than
0.015 for the 99% level of confidence.
n  2317
14. For a random sample of 20 washing machines, the mean replacement time is 10.2 years,
and the standard deviation is 2.6 years.
a. Determine the “” critical values used in constructing a 95% confidence interval.
 L2  8.907
R2  32.852
b. Calculate the confidence interval limits. Round to one decimal place.
2.0    3.8
15. A study was done to determine how fast drivers were actually going when they were pulled
over and ticketed in a 55 mph zone. A sample of 90 drivers was randomly selected, and the
mean speed was found to be 66.2 mph. Use  = 5.1 mph to construct a 95% confidence
interval to estimate , the mean speed of all ticketed drivers in that zone. Round interval
limits to one decimal place.
66.2  1.1 or 65.1    67.3
16. Use your interval from the previous problem to analyze this statement, made by a person
with little knowledge of statistics: “So basically, if you’re doing less than 65 mph you won’t
get pulled over and ticketed.”
The interval tells us that (we are 95% confident) the mean speed for getting ticketed is
between 65.1 and 67.3 mph. There are surely some drivers doing less than 65 that get
ticketed, and some drivers doing more than 67 that get ticketed.
17.