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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Describe the indicated sampling distribution model.
1) Suppose that the national mean weight for a three-year-old girl is 30 pounds with a standard
deviation of 3 pounds. A pediatric office takes a random sample of 100 three -year-old girls,
records their weights, and finds the mean. Describe the sampling distribution model of this mean.
A) Binom(30, 3)
B) N(30, 0.3)
C) There is not enough information to describe the distribution.
D) N(30, 3)
E) N(30, 0.03)
2) Some real estate specialists estimate that the length of time people live in a house has a mean of 10
years and a standard deviation of 3 years. A random sample of 200 families was chosen and
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surveyed. Let y represent the mean number of years that those families had lived in their house.
Describe the sampling distribution model of this mean.
A) N(10, 3)
B) There is not enough information to describe the distribution.
C) N(10, 1.5)
D) Binom(10, 3)
E) N(10, 0.2)
Find the specified probability, from a table of Normal probabilities.
3) The number of hours per week that high school seniors spend on homework is normally
distributed, with a mean of 10 hours and a standard deviation of 3 hours. 60 students are chosen at
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random. Let y represent the mean number of hours spent on homework for this group. Find the
probability that y is between 9.8 and 10.4.
A) 0.547
B) 0.5161
C) 0.080
D) 0.3043
E) 0.1528
4) The weight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine
puts in the boxes is believed to have a Normal model with mean 16.15 ounces and standard
deviation 0.3 ounces. What is the probability that the mean weight of a 50-box case of crackers is
above 16 ounces?
A) 0.0004
B) 0.9998
C) 0.9994
D) 0.9996
E) 0.0002
Solve the problem.
5) The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3
oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume
less than 32 oz?
A) 40.13%
B) 47.15%
C) 59.87%
D) 38.21%
E) 9.87%
Find the specified probability, from a table of Normal probabilities.
6) A restaurantʹs receipts show that the cost of customersʹ dinners has a skewed distribution with a
mean of $54 and a standard deviation of $18. What is the probability that the next 100 customers
will spend an average of at least $58 on dinner?
A) 0.0132
B) 0.0562
C) 0.4121
D) 0.9868
E) 0.5879
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6)
Write the null and alternative hypotheses you would use to test the following situation.
7) An entomologist writes an article in a scientific journal which claims that fewer than 22% of male
fireflies are unable to produce light due to a genetic mutation.
A) H0 : p = 0.22
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HA: p > 0.22
B) H0 : p > 0.22
HA: p < 0.22
C) H0 : p > 0.22
HA: p = 0.22
D) H0 : p < 0.22
HA: p = 0.22
E) H0 : p = 0.22
HA: p < 0.22
8) A weight loss center provided a loss for 72% of its participants. The centerʹs leader decides to test a
new weight loss strategy to see if itʹs better. What are the null and alternative hypotheses?
A) H0 : p > 0.72
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HA: p = 0.72
B) H0 : p = 0.72
HA: p ≠ 0.72
C) H0 : p = 0.72
HA: p > 0.72
D) H0 : p > 0.72
HA: p < 0.72
E) H0 : p = 0.72
HA: p < 0.72
9) The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for
the month in the U.S. and claims the unemployment has not changed in the last two months.
However, the states statistics reveal that there is a change in the U.S. unemployment rate. What are
the null and alternative hypotheses?
A) H0 : p < 0.053
HA: p = 0.053
B) H0 : p ≠ 0.053
HA: p = 0.053
C) H0 : p = 0.053
HA: p > 0.053
D) H0 : p = 0.053
HA: p ≠ 0.053
E) H0 : p > 0.053
HA: p < 0.053
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9)
Construct the requested confidence interval from the supplied information.
10) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly
selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct the 95% confidence interval for the mean score of all such subjects.
A) (74.6, 77.8)
B) (64.2, 88.2)
C) (69.2, 83.2)
D) (64.2, 83.2)
E) (67.7, 84.7)
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11) A savings and loan association needs information concerning the checking account balances of its
local customers. A random sample of 14 accounts was checked and yielded a mean balance of
$664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean
checking account balance for local customers.
A) ($493.71, $834.57)
B) ($453.56, $874.72)
C) ($492.52, $835.76)
D) ($455.65, $835.76)
E) ($455.65, $872.63)
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12) A sample of 81 statistics students at a small college had a mean mathematics ACT score of 26 with
a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for
all statistics students at this college.
B) (25.9, 26.1)
C) (25.3, 26.7)
D) (24.7, 27.3)
E) (25.3, 26.1)
A) (78.6, 83.4)
12)
Interpret the confidence interval.
13) Analysis of a random sample of 250 Illinois nurses produced a 95% confidence interval for the
mean annual salary of $42,838 < μ(Nurse Salary) < $49,691.
A) If we took many random samples of Illinois nurses, about 95% of them would produce this
confidence interval.
B) We are 95% confident that the average nurse salary in the U.S. is between $42,838 and
$49,691.
C) About 95% of the nurses surveyed earn between $42,838 and $49,691.
D) We are 95% confident that the interval from $42,838 to $49,691 contains the true mean salary
of all Illinois nurses.
E) About 95% of Illinois nurses earn between $42,838 and $49,691.
14) A random sample of clients at a weight loss center were given a dietary supplement to see if it
would promote weight loss. The center reported that the 100 clients lost an average of 46 pounds,
and that a 95% confidence interval for the mean weight loss this supplement produced has a
margin of error of ±9 pounds.
A) 95% of the clients in the study lost between 37 and 55 pounds.
B) We are 95% confident that the mean weight loss produced by the supplement in weight loss
center clients is between 37 and 55 pounds.
C) 95% of the people who use this supplement will lose between 37 and 55 pounds.
D) We are 95% sure that the average weight loss among the clients in this study was between 37
and 55 pounds.
E) The average weight loss of clients who take this supplement will be between 37 and 55
pounds.
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13)
14)
Determine the margin of error in estimating the population parameter.
15) Based on a sample of size 49, a 95% confidence interval for the mean score of all students on an
aptitude test is from 64.3 to 69.7.
A) 0.76
B) 5.4
C) 2.7
D) 0.05
E) Not enough information is given.
Write the null and alternative hypothesis.
16) You are considering moving to Atlanta, and are concerned about the average one -way commute
time. Does the average one-way commute time exceed 25 minutes? You take a random sample of
50 Atlanta residents and find an average commute time of 29 minutes with a standard deviation of
7 minutes.
A) H0 : μ = 25
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HA: μ < 25
B) H0 : μ = 29
HA: μ < 29
C) H0 : μ = 25
HA: μ ≠ 25
D) H0 : μ = 29
HA: μ > 29
E) H0 : μ = 25
HA: μ > 25
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and
final conclusion that addresses the original claim.
17)
17) The health of employees is monitored by periodically weighing them in. A sample of 54
employees has a mean weight of 183.9 lb. Assuming that σ is known to be 121.2 lb, use a
0.10 significance level to test the claim that the population mean of all such employees
weights is less than 200 lb.
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Answer Key
Testname: SAMPLE EXERCISES CLT
1) B
2) E
3) A
4) B
5) A
6) A
7) E
8) C
9) D
10) E
11) B
12) D
13) D
14) B
15) C
16) E
17) H0 : μ = 200; H1 : μ < 200; Test statistic: z = -0.98. P-value: 0.1635. Fail to reject H0 . There is not sufficient evidence to
warrrant the rejection of the claim that the mean equals 200.
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