Download ± 2.37 1.96(1.16) 20 ± (1.16) 2.37 20 ± (1.16) 2.37 400 ± 1.96(1.16

Chapter 7 Test
AP Statistics-Adams
Name: ____________________________
Period: _____ Date: _________________
Identify whether the statements in Questions 1–4 are true or false. If false, explain why.
1. The sampling distributions of both proportions and means are always approximately normal.
2. When comparing sampling distributions of sample proportions, for any given sample size n,
the standard error for p = 0.8 is less than for p = 0.5.
3. For any given sample size n, the sampling distribution of the sample proportion when p = 0.2
is more skewed than the sampling distribution of the sample proportion when p = 0.5.
4. For two values taken randomly from two populations, the variance of the sampling distribution
of the difference is equal to the sum of the variances.
5. Which of these statements is not true?
A. One purpose of creating sampling distributions is to observe how a statistic, such as a
sample mean, varies in repeated sampling from the same population.
B. For purposes of generating a sampling distribution, it doesn’t matter much whether you
sample with or without replacement as long as the sample size is small compared to the
population size.
C. It is appropriate to use the normal approximation for a sampling distribution of the sample
proportion if n = 80 and p = 0.05.
D. The spreads of the sampling distributions for sample proportions decrease as the sample
size increases for any fixed value of p, the population proportion.
E. If a population proportion p is close to 0 or 1, then the sample size must be relatively large
to produce an approximately normal sampling distribution for the sample proportion.
6. The distribution of SAT II math scores is approximately normal with mean 660 and standard
deviation 90. The probability that 100 randomly selected students will have a mean SAT II
math score greater than 670 is approximately
A. less than 0.0001
B. 0.1333
D. 0.4558
E. 0.5442
C. 0.2665
7. The distribution of the number of television sets per household in the United States is
approximately normal with mean 2.37 and standard deviation 1.16. The interval of reasonably
likely sample means for samples of size 400 is approximately
A.
2.37 ± 1.96(1.16)
20
B. 2.37 ±
(1.16)
20
1.96(1.16)
20
E. 2.37 ±
1.96(1.16)
400
D. 2.37 ±
C. 2.37 ±
(1.16)
400
8. About 80% of U.S. residents are right-handed.
a. In a random sample of 500 residents, what range of numbers of right-handed residents is
reasonably likely?
b. If 1000 residents are selected at random, would it be unusual to find that less than 77% of
the residents in the sample are right-handed? Explain your reasoning and show
calculations.
9. An investigator anticipates that the proportion of orange blossoms in his hybrid plants is 0.20.
In a random sample of 50 of his plants, 24% of the blossoms are orange. If the investigator is
correct, the standard deviation of the sampling distribution of the sample proportion for a
random sample of 50 plants is approximately
A. 0.060
B. 0.057
C. 2.82
D. 3.02
E. cannot be determined
10. The distribution of GRE analytical reasoning scores is approximately normal with mean 560
and standard deviation 140, and the distribution of GRE verbal reasoning scores is
approximately normal with mean 470 and standard deviation 120.
a. Suppose one GRE analytical reasoning score is selected at random, one GRE verbal
reasoning score is independently selected at random, and the scores are added. Describe
the sampling distribution of this sum in terms of shape, center, and spread.
b. Compute the probability that the sum of the scores from part a is greater than 1250.
c. What is the probability that the verbal reasoning score is at least 200 points higher than
the analytical reasoning score?
d. What is the probability that the sum of 20 randomly and independently selected verbal
reasoning scores is less than 9000?
11. A newly replaced light bulb is used until it burns out and then is replaced immediately by
another. The two bulbs are selected randomly from a large lot of bulbs that the manufacturer
says have an approximately normal lifetime distribution with a mean of 800 hours and a
standard deviation of 100 hours.
a. Describe the distribution of the total lifetime of the two bulbs used in sequence.
b. What is the probability that the sum of the two lifetimes exceeds 1800 hours?
c. What is the probability that the sum of the lifetimes of nine such bulbs selected at random
and burned sequentially exceeds 8100 hours?
d. What is the probability that the second light bulb in the sequence burns longer than the
first?