Download Chapter 7 Review Worksheet

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1. A highway department painted test strips across heavily traveled roads in 8
locations and counters showed that they deteriorated after having been crossed by
142,600
167800
136500
108300
126400
133700
162000
149400
cars. Construct a 95% confidence interval for the average amount of traffic the
new white paint can withstand before it deteriorates.
2. While performing a task under simulated weightlessness, the pulse rate of 12
astronauts increased on the average by 27.33 beats per minute with a std. dev. Of
4.28 beats per minute. If we use X = 27.33 as an estimate of the true average
increase of the pulse rate of astronauts performing the given task, what can we
assert with 99% confidence about the maximum error?
3. If 64% of an SRS of 550 people leaving a shopping mall claim to have spent over
$25, determine a 99% confidence interval estimate for the proportion of shopping
mall customers who spend over $25.
4. In a simple random sample of machine parts, 18 out of 225 were found to have
been damaged in shipment. Establish a 95% confidence interval estimate for the
proportion of machine parts that are damaged in shipment.
5. A bottling machine is operating with a standard deviation of .12 ounce. Suppose
that in an SRS of 36 bottles the machine inserted an average of 16.1 ounces into
each bottle.
a. Give an interval within which we are 95% certain that the mean lies.
b. Calculate a 99% confidence interval.
6. To study the metabolism of insects, researchers fed cockroaches measured
amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the
cockroaches and measured the sugar in various tissues. Five of them had this
much D-glucose in their hindguts after 10 hours:
55.59 68.24 52.73 21.50 23.78
Find the 95% confidence interval for the mean amount of D-glucose.
7. Use the given degree of confidence and sample data to find a confidence interval
for the population standard deviation  (assume the pop. has a normal dist.):
a. GPA’s: 99% confidence, n = 15, X = 2.76, s = 0.88
b. Test scores: 90% confidence; n = 16, X = 77.6, s = 14.2
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8. Suppose a large telephone manufacturer that entered the post-regulation market
quickly has an initial problem with excessive customer complaints and
consequent returns of the phones for repair. The manufacturer wants to estimate
the magnitude of the problem in order to design a quality control program. How
many phones should be sampled and checked in order to estimate the fraction
defective p to within .01 with 90% confidence?
9. Unoccupied seats on flights cause airlines to lose revenue. Suppose an airline
wants to estimate its average number of unoccupied seats per flight over the past
year. The records of 225 flights are randomly selected, and the number of
unoccupied seats is noted for each of the sampled flights. Let X = 11.6 seats and s
= 4.1 seats. Estimate  , the mean number of unoccupied seats per flight during
the past year, using a 90% confidence interval.
10. Name the 3 conditions for using the t-distribution
11. What’s the best point estimate for  ?
12. Assuming that you plan to construct a confidence interval for population mean  ,
use the given data to determine whether the margin of error should be calculated
using the normal distribution, the t-distribution, or neither. Explain why!
a. n = 60, X = 80.5, s = 12.8, and the distribution is skewed.
b. n = 20, X = 87.8, s = 14.2, and the distribution is bell-shaped.
c. n = 25, X = 60.2,  = 14.2, and the distribution is bell-shaped.
#’s 13 and 14: Use the given degree of confidence and sample data to find:
a) The margin of error and b) the confidence interval for  . (Assume that the
distribution is normal)
13. Heights of women: 95% confidence, n = 50, X = 63.4 in, s = 2.4 in
14. Heights of women: 95% confidence, n = 10, X = 63.4 in, s = 2.4 in
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