Question 1

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 _______.

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 2

Suppose a population has a mean of 870 and a variance of 8,100.If a random sample of size 36 is drawn from the population,the probability that the sample mean is between 840 and 900 is _______.

Accepted Answer

The standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size: sqrt(8100/36) = 15. The z-scores for 840 and 900 are (840-870)/15 = -2 and (900-870)/15 = 2, respectively. The probability of a z-score between -2 and 2 is approximately 0.9544.

Question 3

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

Accepted Answer

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

Question 4

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 _______.

Accepted Answer

The standard error of the mean (SEM) is calculated as the population standard deviation divided by the square root of the sample size: SEM = 24 / √144 = 2. The z-score for a sample mean of 404.5 is (404.5 - 400) / 2 = 2.25. Using the standard normal distribution table, the probability of a z-score greater than 2.25 is approximately 0.0122.

Question 5

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 _______.

Accepted Answer

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

Question 6

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 _______.

Accepted Answer

According to the central limit theorem, the mean of all sample means is equal to the population mean, which is given as 80 in this case. Therefore, the answer is (C) 80.

Question 7

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 ________________.

Accepted Answer

Abel's sample is proportionate stratified because he is dividing the population (workers in each department) into subgroups based on a relevant characteristic (department) and then taking a random sample from each subgroup that is proportional to its size (10% of workers in each department). This will ensure that he has representation from each department in his sample and can accurately compare absenteeism rates between departments.

Question 8

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 less than 402 is _______.

Accepted Answer

The sampling distribution of the sample means will have a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:

standard deviation = 24 / sqrt(144) = 2

To find the probability of drawing a sample with a mean less than 402, we need to standardize the sample mean using the formula:

z = (sample mean - population mean) / standard deviation

z = (402 - 400) / 2 = 1

Using a standard normal distribution table or calculator, we can find that the probability of drawing a sample with a z-score less than 1 is approximately 0.8413. Therefore, the answer is choice C.

Question 9

Suppose a population has a mean of 870 and a variance of 1,600.If a random sample of size 64 is drawn from the population,the probability that the sample mean is between 860 and 875 is _______.

Accepted Answer

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

Question 10

Suppose a population has a mean of 450 and a variance of 900.If a random sample of size 100 is drawn from the population,the probability that the sample mean is between 448 and 453 is _______.

Accepted Answer

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

Question 11

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 _______.

Accepted Answer

The probability of drawing a sample with a mean between 395.5 and 404.5 is 0.9756. This is because the mean of the sample will be normally distributed with a mean of 400 and a standard deviation of 24/sqrt(144) = 6. So, the z-score for a mean of 395.5 is (395.5 - 400) / 6 = -0.75, and the z-score for a mean of 404.5 is (404.5 - 400) / 6 = 0.75. The probability of drawing a sample with a mean between these two z-scores is 0.9756.

Question 12

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 _______.

Accepted Answer

The standard deviation of sample means is equal to the population standard deviation divided by the square root of the sample size. Therefore, the standard deviation of sample means would equal 80/√100 = 8.

Question 13

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 _____________.

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 14

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 _______.

Accepted Answer

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

Question 15

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 _____________.

Accepted Answer

Catherine's sample is a convenience sample because she chose her closest friends rather than selecting participants at random or using a predetermined sampling method. A convenience sample is often quick and easy to obtain, but it may not be representative of the population being studied.

Question 16

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 _______.

Accepted Answer

We can use the central limit theorem to determine the probability of drawing a sample with a mean of more than $115. 
The sample size (n) is 49, which is greater than 30, so the sample mean will be approximately normally distributed. 
The mean of the sampling distribution of the sample means will be equal to the population mean, which is $110. 
The standard deviation of the sampling distribution of the sample means, also known as standard error, will be equal to the population standard deviation divided by the square root of the sample size, which is 18/sqrt(49) = 2.571. 
Now we can standardize the sample mean:

Z = (X - μ) / (σ / sqrt(n)) 
Z = (115 - 110) / (18/sqrt(49)) 
Z = 2.193

Using a standard normal distribution table or calculator, we can find the probability of Z being greater than 2.193:

P(Z > 2.193) = 0.0156

Therefore, the probability of drawing a sample with a mean of more than $115 is 0.0156 or approximately 0.0262 (rounded to four decimal places), which corresponds to choice C.

Question 17

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 _______.

Accepted Answer

The sampling distribution of the sample mean will be normally distributed with mean $110 and standard deviation $18/sqrt(49) = $2.57. We calculate the z-scores for $100 and $115, then find the probability between these z-scores using the standard normal distribution table. The probability corresponds to 0.9738.

Question 18

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 _______.

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 19

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 _______.

Accepted Answer

The central limit theorem states that if a sample of size n is drawn from a population with mean µ, then as n increases, the distribution of sample means approaches a normal distribution with a mean of µ. Therefore, the mean of all sample means would be equal to the population mean, which is 16 in this case.

Question 20

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 ________________.

Accepted Answer

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

Quiz 7: Sampling and Sampling Distributions