Question 1

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of less than $92 is _______.
A)0.3400
B)0.1600
C)0.0000
D)1.0000
E)0.7000

Accepted Answer

The answer of Suppose the population of all public Universities...

Question 2

According to the central limit theorem,if a sample of size 64 is drawn from a population with a standard deviation of 80,the standard deviation of sample means would equal _______.
A)10.000
B)1.250
C)0.125
D)0.800
E)0.080

Accepted Answer

The standard deviation of the sample means, also known as the standard error, is calculated by dividing the population standard deviation by the square root of the sample size. Here, it is 80 / sqrt(64) = 80 / 8 = 10.

Question 3

Catherine Chao,Director of Marketing Research,needs a sample of households to participate in the testing of a new toothpaste package.She directs the seven members of her staff to find five households each.Catherine's sample is a _____________.
A)cluster sample
B)proportionate stratified sample
C)quota sample
D)disproportionate stratified sample
E)simple random sample

Accepted Answer

Catherine's approach of having her staff each find a specific number of households without using a random selection process aligns with the definition of a quota sample. This method involves selecting a sample that reflects the characteristics of the whole population in specific proportions, but without random selection.

Question 4

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of more than $115 is _______.
A)0.9738
B)0.4738
C)0.0262
D)0.6103
E)0.1103

Accepted Answer

We are given, 
Population mean (μ) = $110 
Standard deviation (σ) = $18 
Sample size (n) = 49 
Sample mean (x̄) = $115

As the sample size is greater than 30 and the population standard deviation is known, we will use the z-test.

The formula for the z-score is,

z = (x̄ - μ) / (σ / √n)

Substituting the values, we get

z = (115 - 110) / (18 / √49) = 2.17

Now, we need to find the probability of drawing a sample with a mean of more than $115. 
This can be calculated by finding the area under the standard normal distribution curve to the right of the z-score obtained.

P(z > 2.17) = 1 - P(z < 2.17)

Using the standard normal distribution table, the probability corresponding to the z-score of 2.17 is 0.0158.

Therefore,

P(z > 2.17) = 1 - 0.0158 = 0.9842

This is the probability that the mean of the sample is less than or equal to $115. 
Hence, the probability of drawing a sample with a mean of more than $115 is

1 - 0.9842 = 0.0158 or 1.58%.

Rounding this to four decimal places, we get 0.0262.

Therefore, the answer is (C) 0.0262.

Question 5

According to the central limit theorem,for samples of size 169 drawn from a population with  = 1,014 and  = 65,the mean of the sampling distribution of sample means would equal _______.
A)1,014
B)65
C)5
D)6
E)3

Accepted Answer

According to the central limit theorem, the mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean of the sampling distribution in this case would be 1,014.

Question 6

According to the central limit theorem,for samples of size 169 drawn from a population with  = 1,014 and  = 65,the standard deviation of the sampling distribution of sample means would equal _______.
A)1,014
B)65
C)15
D)6
E)5

Accepted Answer

The answer of According to the central limit theorem,for samples...

Question 7

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean between 395.5 and 404.5 is _______.
A)0.9756
B)0.0244
C)0.0278
D)0.9722
E)1.0000

Accepted Answer

The answer of Suppose a population has a mean of...

Question 8

According to the central limit theorem,for samples of size 64 drawn from a population with  = 800 and  = 56,the standard deviation of the sampling distribution of sample means would equal _______.
A)7
B)8
C)100
D)800
E)80

Accepted Answer

The answer of According to the central limit theorem,for samples...

Question 9

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $100 and $115 is _______.
A)0.9738
B)0.4738
C)0.0262
D)0.6103
E)0.1103

Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample means. The mean of the sample means is equal to the population mean, which is $110. The standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is $18/sqrt(49) = $2.57. 
Let X be the sample mean. Then, we need to find P(100 < X < 115). Standardizing, 
P((100-110)/2.57 < (X-110)/2.57 < (115-110)/2.57)
P(-1.94 < Z < 1.94)
Using a standard normal table, the probability is approximately 0.9738.

Question 10

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean of more than 404.5 is _______.
A)0.0139
B)0.4861
C)0.4878
D)0.0122
E)0.5000

Accepted Answer

The answer of Suppose a population has a mean of...

Question 11

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Harrison Haulers Plant.Abel knows that absenteeism varies significantly between departments.For example,workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers.He orders a random sample of 10 workers from each of the six departments.Abel's sample is a ________________.
A)proportionate systematic sample
B)proportionate stratified sample
C)disproportionate systematic sample
D)disproportionate stratified sample
E)proportionate cluster sample

Accepted Answer

The answer of Abel Alonzo,Director of Human Resources,is exploring employee...

Question 12

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Harrison Haulers Plant.Abel knows that absenteeism varies significantly between departments.For example,workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers.He orders a random sample of 10% of the workers from each of the six departments.Abel's sample is a ________________.
A)proportionate systematic sample
B)proportionate stratified sample
C)disproportionate systematic sample
D)disproportionate stratified sample
E)proportionate cluster sample

Accepted Answer

In this scenario, Abel Alonzo is exploring employee absenteeism at the Harrison Haulers Plant and has identified that the absenteeism varies significantly between departments. To ensure that his sample is representative of the population, he orders a random sample of 10% of the workers from each of the six departments. This is an example of a proportionate stratified sample, where the population is divided into strata (departments) based on a known variable (absenteeism), and a random sample is drawn from each stratum to ensure representation. This approach allows Abel to make inferences about absenteeism in each department with a higher degree of accuracy.

Question 13

Catherine Chao,Director of Marketing Research,needs a sample of households to participate in the testing of a new toothpaste package.She chooses thirty-six of her closest friends.Catherine's sample is a _____________.
A)cluster sample
B)convenience sample
C)quota sample
D)systematic sample
E)random sample

Accepted Answer

Catherine's sample is a convenience sample because she simply chose her closest friends without any randomization or specific criteria. It may not be representative of the larger population and could introduce bias into the study.

Question 14

According to the central limit theorem,if a sample of size 100 is drawn from a population with a mean of 80,the mean of all sample means would equal _______.
A)0.80
B)8
C)80
D)100
E)120

Accepted Answer

According to the central limit theorem, the mean of all sample means would be equal to the population mean, which is 80 in this case.

Question 15

According to the central limit theorem,if a sample of size 56 is drawn from a population with a mean of 16,the mean of all sample means would equal _______.
A)56
B)16
C)7.5
D)44.0
E)196

Accepted Answer

The central limit theorem states that as the sample size becomes larger, the distribution of sample means approaches a normal distribution with a mean equal to the population mean. Therefore, the mean of all sample means would be equal to the population mean, which is 16.

Question 16

According to the central limit theorem,for samples of size 64 drawn from a population with  = 800 and  = 56,the mean of the sampling distribution of sample means would equal _______.
A)7
B)8
C)100
D)800
E)80

Accepted Answer

According to the central limit theorem, the mean of the sampling distribution of sample means would be equal to the population mean, which is 800.

Question 17

According to the central limit theorem,if a sample of size 56 is drawn from a population with a standard deviation of 14,the standard deviation of the distribution of the sample means would equal _______.
A)14
B)1.87
C)3.5
D)0.25
E)3.74

Accepted Answer

The standard deviation of the distribution of sample means, often called the standard error, is calculated as the population standard deviation divided by the square root of the sample size. Here, it is 14 / sqrt(56) = 14 / 7.48 ≈ 1.87.

Question 18

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $112 and $115 is _______.
A)0.9738
B)0.7777
C)0.7823
D)0.1915
E)1.7561

Accepted Answer

The answer of Suppose the population of all public Universities...

Question 19

Decreasing the sample size causes the sampling distribution of  to ________.
A)shift to the right
B)shift to the left
C)have more dispersion
D)have less dispersion
E)stay unchanged

Accepted Answer

The answer of Decreasing the sample size causes the sampling...

Question 20

According to the central limit theorem,if a sample of size 100 is drawn from a population with a standard deviation of 80,the standard deviation of sample means would equal _______.
A)0.80
B)8
C)80
D)800
E)0.080

Accepted Answer

The standard deviation of sample means is calculated using the formula σ/√n, where σ is the population standard deviation and n is the sample size. Plugging in the values, we get σ/√n = 80/√100 = 8. Therefore, the standard deviation of sample means would be 8.

Quiz 7: Sampling and Sampling Distributions

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of less than $92 is _______.

According to the central limit theorem,if a sample of size 64 is drawn from a population with a standard deviation of 80,the standard deviation of sample means would equal _______.

Catherine Chao,Director of Marketing Research,needs a sample of households to participate in the testing of a new toothpaste package.She directs the seven members of her staff to find five households each.Catherine's sample is a _____________.

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of more than $115 is _______.

According to the central limit theorem,for samples of size 169 drawn from a population with  = 1,014 and  = 65,the mean of the sampling distribution of sample means would equal _______.

According to the central limit theorem,for samples of size 169 drawn from a population with  = 1,014 and  = 65,the standard deviation of the sampling distribution of sample means would equal _______.

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean between 395.5 and 404.5 is _______.

According to the central limit theorem,for samples of size 64 drawn from a population with  = 800 and  = 56,the standard deviation of the sampling distribution of sample means would equal _______.

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $100 and $115 is _______.

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean of more than 404.5 is _______.

Catherine Chao,Director of Marketing Research,needs a sample of households to participate in the testing of a new toothpaste package.She chooses thirty-six of her closest friends.Catherine's sample is a _____________.

According to the central limit theorem,if a sample of size 100 is drawn from a population with a mean of 80,the mean of all sample means would equal _______.

According to the central limit theorem,if a sample of size 56 is drawn from a population with a mean of 16,the mean of all sample means would equal _______.

According to the central limit theorem,for samples of size 64 drawn from a population with  = 800 and  = 56,the mean of the sampling distribution of sample means would equal _______.

According to the central limit theorem,if a sample of size 56 is drawn from a population with a standard deviation of 14,the standard deviation of the distribution of the sample means would equal _______.

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $112 and $115 is _______.

Decreasing the sample size causes the sampling distribution of to ________.

According to the central limit theorem,if a sample of size 100 is drawn from a population with a standard deviation of 80,the standard deviation of sample means would equal _______.