Chapter 9 Review Assignment 1. A study of voting chose 663 registered voters at random after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers? a. 72% is a sample; 56% is a population b. 72% and 56% are both statistics c. 72% is a statistic and 56% is a parameter d. 72% is a parameter and 56% is a statistic e. 72% and 56% are both parameters 2. The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking. The effect of this increase is to a. Reduce the bias of the estimate b. Increase the bias of the estimate c. Reduce the variability of the estimate d. Increase the variability of the estimate e. Have no effect since the population size is the same 3. Suppose we select an SRS of size n = 100 from a large population having proportion p successes. Let p̂ be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p̂ ? a. 0.01 b. 1/11 c. 0.85 d. 0.975 e. 0.999 4. The distribution of values taken by a statistic in all possible samples of the same size from the same population is a. The probability that the statistic is obtained b. The population parameter c. The variance of the values d. The sampling distribution of the statistic 5. The Central Limit Theorem is important in statistics because it allows you to use the Normal distribution to make inferences concerning the population mean a.
b.
c.
d.
If the sample size is reasonably large (for any population). If the population is normally distributed and the sample size is reasonable large If the population is normally distributed (for any sample size) If the population is normally distributed and the population variance is known for any sample size e. If the population size is reasonably large (whether the population distribution is known or not). Chapter 9 Review Assignment 6. Which of the following statements about the sampling distribution of the sample mean is incorrect? a. The standard deviation of the sampling distribution will decrease as the sample size increases b. The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples of the same size c. The sampling distribution shows how the sample mean will vary in repeated samples of the same size d. The sampling distribution shows how the sample was distributed around the sample mean. 7. A random sample of size 25 is to be taken from a population which is normally distributed with mean 60 and standard deviation 10. The sampling distribution of x is a. Exactly normal with mean 60 and standard deviation 10 b. Approximately normal with mean 60 and standard deviation 2 c. Approximately normal with mean 60 and standard deviation 0.4 d. Exactly with mean 12 and standard deviation 2 Use the following information to answer questions 8 and 9.
An automobile insurer has found that repair claims have a mean of $920 and a standard
deviation of $870. Suppose that the next 100 claims can be regarded as a random sample
from the long-run claims process.
8. The mean and standard deviation of the mean of the next 100 claims is
a. mean = $920 and standard deviation = $87.
b. mean = $920 and standard deviation = $8.70.
c. mean = $92 and standard deviation = $87.
d. mean = $92 and standard deviation = $870.
e. none of these.
9. The probability that the mean of the next 100 claims is larger than $1000 is
approximately
a. 0.9200.
b. 0.8212.
c. 0.1788.
d. 0.0800.
e. close to 0
Chapter 9 Review Assignment 10. The student newspaper at a large university asks an SRS of 250 undergraduates, “Do
you favor eliminating the carnival from the end of term celebration?” All in all, 150
of the 250 graduates are in favor. Suppose that (unknown to you) 55% of all
undergraduates favor eliminating the carnival. If you took a very large number of
random samples, of size n =250 from this population, the sampling distribution of the
sample proportion p̂ would be
(a) heavily skewed with mean 0.55 and standard deviation 0.03
(b) exactly normal with mean 0.60 and standard deviation 0.03
(c) approximately normal with mean 0.55 and standard deviation 0.03
(d) heavily skewed with mean 0.60 and standard deviation 0.03
11. It is generally believed that nearsightedness affects about 12% of children. A
school district gives vision tests to 133 randomly selected incoming kindergarten
children.What percent of such samples would you expect to have less than 10% of the
children be nearsighted?
(a) 23.89%
(b) 2.82%
(c) 2.60%
(d) 22.10%
12. In a test of ESP (extrasensory perception), the experimenter looks at cards that are
hidden from the subject. Each card contains one of four figures—a star, a circle, a wavy
line, or a square. An experimenter looks at each of 100 cards in turn, and the subject tries
to read the experimenter’s mind and name the shape on each card. What is the
approximate probability that the subject gets more than 30 correct if the subject does not
have ESP and is just guessing?
A. 0.3121.
B. 0.2483.
C. 0.1251.
D. 0.0427.
E. <0.001.
Chapter 9 Review Assignment 1.) A summer resort rents rowboats to customers but does not allow
more than four people. Each boat is designed to hold no more than 800
pounds. Suppose the distribution of adult males who rent boats is,
including their clothes and gear, normal with a mean of 190 pounds and
a standard deviation of 10 pounds. If the weights of individual
passengers are independent, what is the probability that a group of
four adult male passengers will exceed the acceptable weight limit of
800 pounds?
2.) The insurance company sees that in the entire population of
homeowners, the mean loss from fire µ = $250 and the standard
deviation of the loss is σ = $300 . The distribution of losses is strongly
right skewed: many policies have $0 loss, but a few have large losses.
If the company randomly samples 10,000 policies, what is the
probability that the average loss will be greater than $260?
Chapter 9 Review Assignment 3.) Suppose that 47% of adult women think they do not get enough time
for themselves. An opinion poll interviews 1025 randomly chosen
women and records the sample proportion who feel they do not get
enough time for themselves. What is the probability that the poll gets
a sample in which fewer than 45% say they do not get enough time for
themselves.
Chapter 9 Review Assignment 4.) Voter registration records show that 68% of all voters in Indianapolis
are registered as Republicans. You use a random digit dialing service
to contact a random sample of 150 voters in Indianapolis. Find the
probability of obtaining an SRS of 150 from the population of
Indianapolis voters in which 73% or more are registered Republicans.
5.) The level of nitrogen oxide (NOX) in the exhaust of a particular car
model varies with a mean 1.4 grams/mile and standard deviation 0.3
grams/mile. A company has 125 cars of this model in its fleet. If x is
the mean NOX emission level for these 125 cars, what is the level L
such that the probability that x is greater than L is only .01?
Chapter 9 Review Assignment 6.) The weight of eggs produced by a certain breed of hen is normally
distributed with a mean of 65 grams and a standard deviation 5.
a. Find the probability that the weight of a randomly selected egg
from this certain breed of hen exceeds 70 grams.
b. Find the probability that a random sample of 8 eggs from this
certain breed of hen has a mean weight that exceeds 70 grams.
c.
If the weights of individual eggs are independent, what is the
probability that the weight of the 12 eggs in a carton have a
total weight that exceeds 825 grams.