Question 1

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 closest to _______.
A)0.9756
B)0.0244
C)0.0278
D)0.9722
E)1.0000

Accepted Answer

Using the Central Limit Theorem, we can calculate the probability of drawing a sample with a mean between 395.5 and 404.5. The standard error (SE) of the sample mean is the population standard deviation divided by the square root of the sample size, which is 24 / sqrt(144) = 24 / 12 = 2. To find the Z-scores for 395.5 and 404.5, we subtract the population mean (400) and divide by the SE. For 395.5, Z = (395.5 - 400) / 2 = -2.25. For 404.5, Z = (404.5 - 400) / 2 = 2.25. Looking these Z-scores up in a standard normal distribution table gives us the probabilities of 0.0122 and 0.9878, respectively. The probability of the sample mean being between 395.5 and 404.5 is the difference, 0.9878 - 0.0122 = 0.9756.

Question 2

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 sample is a disproportionate stratified sample because Abel is taking an equal number of workers (10) from each department, regardless of the department's size, which means the sample is not proportionate to the department sizes.

Question 3

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

Abel's approach of selecting a 10% sample from each department, acknowledging the variation in absenteeism and department sizes, aligns with the definition of a proportionate stratified sample. This method involves dividing the population into strata (departments, in this case) and sampling a proportionate number of participants from each stratum.

Question 4

According to the central limit theorem, for samples of size 169 drawn from a population with μ = 1,014 and σ = 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 standard deviation of the sampling distribution of sample means (standard error) is calculated as σ/√n, which is 65/√169 = 65/13 = 5.

Question 5

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 6

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 closest to _______.
A)0.0139
B)0.4861
C)0.4878
D)0.0122
E)0.5000

Accepted Answer

The probability of drawing a sample with a mean of more than 404.5 can be found using the Z-score formula for a sample mean: $Z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n}}$, where $\bar{X}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $Z = \frac{404.5 - 400}{24/\sqrt{144}} = \frac{4.5}{2} = 2.25$. Looking up 2.25 in the Z-table gives a right-tail probability of approximately 0.0122.

Question 7

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

Accepted Answer

Decreasing the sample size typically causes the sampling distribution of the sample mean (x̄) to have more dispersion, as smaller samples are less likely to closely approximate the population mean, leading to greater variability in sample means.

Question 8

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 9

Suppose the population of all public Universities shows the annual parking fee per student is normally distributed with a mean of $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 closest to _______.
A)0.9738
B)0.4738
C)0.0262
D)0.6103
E)0.1103

Accepted Answer

Using the Central Limit Theorem, we can calculate the probability of drawing a sample with a mean of more than $115. The standard error (SE) of the sample mean is the population standard deviation divided by the square root of the sample size, which is $18 / \sqrt{49} = $18 / 7 = $2.57. We calculate the Z-score for a sample mean of $115 as follows: Z = ($115 - $110) / $2.57 = $5 / $2.57 ≈ 1.946. Looking up this Z-score in a standard normal distribution table or using a calculator, we find the probability of a Z-score being less than 1.946 is approximately 0.974. Therefore, the probability of a Z-score being more than 1.946 is 1 - 0.974 = 0.026. This gives us the probability of drawing a sample with a mean of more than $115.

Question 10

Suppose the population of all public Universities shows the annual parking fee per student is normally distributed with a mean of $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 closest to _______.
A)0.3400
B)0.1600
C)0.0000
D)1.0000
E)0.7000

Accepted Answer

The standard error of the mean is $18/sqrt(49) = $2.57. The z-score for a sample mean of $92 is (92-110)/2.57 = -7.00. A z-score of -7.00 is extremely low, making the probability effectively 0.

Question 11

According to the central limit theorem, for samples of size 64 drawn from a population with μ = 800 and σ = 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...

Question 12

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 13

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

The central limit theorem states that the mean of all sample means (the sampling distribution of the mean) will equal the population mean. Therefore, if the population mean is 80, the mean of all sample means will also be 80.

Question 14

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 the distribution of sample means will be normally distributed around the population mean. Therefore, the mean of all sample means equals the population mean, which is 16 in this case.

Question 15

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

Accepted Answer

The central limit theorem states that the mean of the sampling distribution of the sample means will be equal to the mean of the population from which the samples are drawn. In this case, the population mean (μ) is 800, so the mean of the sampling distribution of sample means is also 800.

Question 16

Suppose the population of all public Universities shows the annual parking fee per student is normally distributed with a mean of $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 closest to _______.
A)0.9738
B)0.4738
C)0.0262
D)0.6103
E)0.1103

Accepted Answer

Using the Central Limit Theorem, we can calculate the probability of drawing a sample with a mean between $100 and $115. The standard error (SE) of the sample mean is the population standard deviation divided by the square root of the sample size, which is $18 / \sqrt{49} = $18 / 7 = $2.57. To find the Z-scores for $100 and $115, we use the formula Z = (X - μ) / SE, where X is the sample mean, μ is the population mean, and SE is the standard error. For $100, Z = ($100 - $110) / $2.57 = -3.89. For $115, Z = ($115 - $110) / $2.57 = 1.95. Using the Z-table, the probability of Z being between -3.89 and 1.95 is approximately 0.9738.

Question 17

According to the central limit theorem, for samples of size 169 drawn from a population with μ = 1,014 and σ = 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

The central limit theorem states that the mean of the sampling distribution of the sample means will be equal to the mean of the population from which the samples are drawn, which in this case is 1,014.

Question 18

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 choice of thirty-six of her closest friends as a sample is an example of a convenience sample because she selected participants based on their easy availability and proximity to her, rather than using a method that ensures the sample is representative of a larger population.

Question 19

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 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. Therefore, it is 80 / sqrt(100) = 80 / 10 = 8.

Question 20

Suppose the population of all public Universities shows the annual parking fee per student is normally distributed with a mean of $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 closest to _______.
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...

Quiz 7: Sampling and Sampling Distributions

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 closest to _______.

According to the central limit theorem, for samples of size 169 drawn from a population with μ = 1,014 and σ = 65, the standard deviation of the sampling distribution 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 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 closest to _______.

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

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 _______.

According to the central limit theorem, for samples of size 64 drawn from a population with μ = 800 and σ = 56, the standard deviation 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 _______.

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 μ = 800 and σ= 56, 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 μ = 1,014 and σ = 65, the mean of the sampling distribution 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 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 standard deviation of 80, the standard deviation of sample means would equal _______.