Question 1

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-An automotive repair shop has determined that the average service time on an automobile is 2 hours with a standard deviation of 32 minutes. A random sample of 64 services is selected.
a.What is the probability that the sample of 64 will have a mean service time greater than 114 minutes?
b.Assume the population consists of 400 services. Determine the standard error of the mean.

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Question 2

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-The standard error of the proportion will become larger as
A)n increases
B)p approaches 0
C)p approaches .5
D)p approaches 1

Accepted Answer

The standard error of the proportion is largest when p = 0.5 because the formula for the standard error of a proportion is sqrt[p(1-p)/n], and the product p(1-p) reaches its maximum value when p = 0.5.

Question 3

Exhibit 7-4
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-4. The standard error of the mean equals
A)0.3636
B)0.0331
C)0.0200
D)4.000

Accepted Answer

The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size: 0.22 / √121 = 0.02.

Question 4

The life expectancy in the United States is 75 with a standard deviation of 7 years. A random sample of 49 individuals is selected.
a.What is the probability that the sample mean will be larger than 77 years?
b.What is the probability that the sample mean will be less than 72.7 years?
c.What is the probability that the sample mean will be between 73.5 and 76 years?
d.What is the probability that the sample mean will be between 72 and 74 years?
e.What is the probability that the sample mean will be larger than 73.46 years?

Accepted Answer

The answer of The life expectancy in the United States...

Question 5

Exhibit 7-4
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is
A)0.22
B)4
C)121
D)0.02

Accepted Answer

The point estimate of the mean content of all bottles is the same as the sample mean, which is 4 ounces.

Question 6

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-All of the following are true about the standard error of the mean except
A)it is larger than the standard deviation of the population
B)it decreases as the sample size increases
C)its value is influenced by the standard deviation of the population
D)it measures the variability in sample means

Accepted Answer

The standard error of the mean is actually smaller than the standard deviation of the population. It measures the variability in sample means while taking into account the sample size and the standard deviation of the population. As the sample size increases, the standard error of the mean decreases, and a larger standard deviation of the population will increase the standard error of the mean.

Question 7

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-There are 8,000 students at the University of Tennessee at Chattanooga. The average age of all the students is 24 years with a standard deviation of 9 years. A random sample of 36 students is selected.
a.Determine the standard error of the mean.
b.What is the probability that the sample mean will be larger than 19.5?
c.What is the probability that the sample mean will be between 25.5 and 27 years?

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Question 8

Exhibit 7-1
The following data was collected from a simple random sample from a process (an infinite population). 
-Refer to Exhibit 7-1. The mean of the population
A)is 14
B)is 15
C)is 15.1581
D)could be any value

Accepted Answer

Without specific data or context from Exhibit 7-1, the mean of the population cannot be determined and could be any value.

Question 9

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are
A)8.7 and 1.94
B)36 and 1.94
C)36 and 1.86
D)36 and 8

Accepted Answer

The mean of the sampling distribution of the sample means is the same as the mean of the population, which is 36. 
The standard deviation of the sampling distribution of the sample means is calculated by dividing the population standard deviation by the square root of the sample size: 
$ \frac{8}{\sqrt{17}} \approx 1.86$
Therefore, the correct answer is C.

Question 10

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-A simple random sample of 8 employees of a corporation provided the following information.  
a.Determine the point estimate for the average age of all employees.
b.What is the point estimate for the standard deviation of the population?
c.Determine a point estimate for the proportion of all employees who are female.

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Question 11

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-The average weekly earnings of bus drivers in a city are $950 (that is $\mu$) with a standard deviation of $45 (that is  $\sigma$). Assume that we select a random sample of 81 bus drivers.
a.Assume the number of bus drivers in the city is large compared to the sample size. Compute the standard error of the mean.
b.What is the probability that the sample mean will be greater than $960?
c.If the population of bus drivers consisted of 400 drivers, what would be the standard error of the mean?

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Question 12

Exhibit 7-4
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-4. In this problem the 0.22 is
A)a parameter
B)a statistic
C)the standard error of the mean
D)the average content of colognes in the long run

Accepted Answer

The 0.22 ounces represents the standard deviation of the population, which is a fixed and known value. Therefore, it is a parameter.

Question 13

Scores for a standardized test are normally distributed with a mean of 1200 and a standard deviation of 60. A sample of 36 scores is selected.
a.What is the probability that the sample mean will be larger than 1224?
b.What is the probability that the sample mean will be less than 1230?
c.What is the probability that the sample mean will be between 1200 and 1214?
d.What is the probability that the sample mean will be greater than 1200?
e.What is the probability that the sample mean will be larger than 73.46?

Accepted Answer

The answer of Scores for a standardized test are normally...

Question 14

Exhibit 7-3
The following information was collected from a simple random sample of a population. 
-Refer to Exhibit 7-3. The point estimate of the population standard deviation is
A)2.000
B)1.291
C)1.414
D)1.667

Accepted Answer

The point estimate of the population standard deviation is typically calculated using the sample standard deviation formula. If the sample variance is given as 2, the standard deviation would be the square root of 2, which is approximately 1.414.

Question 15

Exhibit 7-2
Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said "yes," and one hundred said "no."
-Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "no" is
A)75
B)0.25
C)0.75
D)0.50

Accepted Answer

The point estimate for the proportion who said "no" is the number who said "no" divided by the total number of respondents, which is:

100/400 = 0.25

Therefore, the best choice is B, 0.25.

Question 16

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.
a.What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean?
b.What is the probability that these 64 students will spend a combined total of more than $715.21?
c.What is the probability that these 64 students will spend a combined total between $703.59 and $728.45?

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Question 17

Exhibit 7-3
The following information was collected from a simple random sample of a population. 
-Refer to Exhibit 7-3. The point estimate of the mean of the population is
A)18.0
B)19.6
C)108
D)sixteen, since 16 is the smallest value in the sample

Accepted Answer

The point estimate of the mean of the population is the sample mean, which is calculated as the average of the sample values.

Question 18

Exhibit 7-2
Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said "yes," and one hundred said "no."
-Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "yes" is
A)300
B)approximately 300
C)0.75
D)0.25

Accepted Answer

The point estimate of the proportion in the population who will respond "yes" is the proportion of the sample who responded "yes." In this case, 300 out of the 400 registered voters surveyed responded "yes," so the point estimate is 300/400 = 0.75. Therefore, the correct answer is C) 0.75.

Question 19

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-Refer to Exhibit 7-5. Which of the following best describes the form of the sampling distribution of the sample mean for this situation?
A)Approximately normal because the sample size is small relative to the population size.
B)Approximately normal because of the central limit theorem.
C)exactly normal
D)None of the alternative answers is correct.

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Question 20

Exhibit 7-5
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.
-Starting salaries of a sample of five management majors along with their genders are shown below.  
a.What is the point estimate for the starting salaries of all management majors?
b.Determine the point estimate for the variance of the population.
c.Determine the point estimate for the proportion of male employees.

Accepted Answer

The answer of Exhibit 7-5
Random samples of size 17 are...

Quiz 7: Sampling and Sampling Distributions

Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. -The standard error of the proportion will become larger as

Exhibit 7-4 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-4. The standard error of the mean equals

Exhibit 7-4 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is

Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. -All of the following are true about the standard error of the mean except

Exhibit 7-1 The following data was collected from a simple random sample from a process (an infinite population) . -Refer to Exhibit 7-1. The mean of the population

Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. -Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are

Exhibit 7-4 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-4. In this problem the 0.22 is

Exhibit 7-3 The following information was collected from a simple random sample of a population. -Refer to Exhibit 7-3. The point estimate of the population standard deviation is

Exhibit 7-2 Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said "yes," and one hundred said "no." -Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "no" is

Exhibit 7-3 The following information was collected from a simple random sample of a population. -Refer to Exhibit 7-3. The point estimate of the mean of the population is

Exhibit 7-2 Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said "yes," and one hundred said "no." -Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "yes" is

Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. -Refer to Exhibit 7-5. Which of the following best describes the form of the sampling distribution of the sample mean for this situation?