Math 52 – Chapter 6
Complete all work on a separate sheet of paper.
1. Suppose that a population consists of the values 6, 8, 4, 12.
a. Construct the table showing all possible samples and sample means for samples
of size 2 chosen with replacement. (10 pts)
b. What is the mean of this sampling distribution? (4 pts)
c. What is the mean of the population? (4 pts)
2. In the year 2000, the mean ACT math score was 20.7, with a standard deviation of 5.
Assume that ACT math scores are normally distributed. (6 pts each)
a. What is the probability that a randomly selected student has an ACT math
score of 18 or less?
b. What is the probability that a random sample of 20 ACT test takers had a mean
math score of 18 or less?
c. Suppose that at a particular school a random sample of 20 ACT test takers had
a mean score of 18 or less, what might you conclude about this result?
d. Explain why the Central Limit Theorem can be applied in this problem.
3. According to advertising by the Energy Efficient Refrigerator Company, the cost to
run their refrigerators is $120 per year with a standard deviation of $17. Suppose that a
random sample of 100 such refrigerators results in an average annual cost of $125. (6
each)
a. What is the probability that a random sample of 100 such refrigerators
would result in a mean cost of $125 per year or more.
b. What does this result tell you about the advertising by the company?
Explain and justify your answer in full sentences.
c. Why does the Central Limit Theorem apply in this problem?
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Chapter 7
Unless otherwise indicated, each problem part is worth 6 points. Be sure to include a
conclusion sentence, your answer is not considered complete without it. You may use the
method of your choice to solve all problems, unless otherwise indicated. Answers must
include appropriate units.
1. The Dunlop tire company wishes to estimate the mean mileage for its SP4000 tires. In
a random sample of 35 tires, the sample mean was 62,450 miles. Assume that the
population standard deviation is known to be 4400 miles.
a. Construct a 95% confidence interval for the mileage for all SP4000 tires.
b. How many tires would Dunlop need in order to estimate the mean mileage
for all SP4000 tires within 3000 miles with 99% confidence?
2. The following data represent the mathematics achievement test scores for a random
sample of 15 students who had just completed high school in Canada and the U.S.,
according to data from the International Association for the Evaluation of Education
Achievement study in 1998.
Canada: 558 556
637 511
594
557
592
531
458
526
600
468
554
614
500
U.S.:
510
553
432
446
500
559
531
410
469
459
450
583 402
465 483
Assume that both come from normally distributed populations.
a. Construct a 99% confidence interval for the population mean achievement
score of Canada.
b. Construct a 99% confidence interval for the population mean achievement
score of the U.S.
c. Does it appear that Canadians scored higher than Americans? EXPLAIN!
Can you defiantly say that Canadians scored higher?
3. A jar of peanuts is supposed to have 16 ounces of peanuts. A quality control manager
randomly selects 12 jars from a filling machine and finds that they have a mean of a
mean of 15.9 ounces and a standard deviation of 0.35 ounces. Assume that the data
comes from a normally distributed population.
a. Construct a 90% confidence interval for the population standard deviation
of the number of ounces of peanuts in a jar.
b. Suppose the quality control manager wants the machine to have a population
standard deviation of below 0.20 ounces. Does the confidence interval
show this. EXPLAIN.
4. In a Harris Poll conducted Feb. 9, 2000, 1247 of 2208 randomly selected American
adults said that they judged that state laws governing child safety seats should be
strengthened.
a. Construct a 92% confidence interval for the percentage of American adults
who say that such laws should be strengthened. Complete this part using
the appropriate formulas and tables. Answers found using the direct
calculator function will receive no partial credit. Show all work. (10 pts)
b. What effect on the interval would raising the confidence level to 96% have?
Do not actually find the interval, just describe what would happen and why.