Chapter 7 Distribution of Sample Means

What is the true standard deviation for 1, 2, 3, 4, 5, and 6?

1.71

When is the distribution of sample means identical to the population distribution? a. When n = 1 b. When the standard error equals the population standard deviation c. When n is a very large number d. Both a and b

Both a and b

True or False The expected value of M, or the mean of the distribution of sample means, is equal to U (population mean)

True

A random sample is obtained from a population with μ = 120 and σ = 20, and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment? a. n = 36 with M = 121 b. n = 36 with M = 123 c. n = 144 with M = 121 d. n = 144 with M = 124

n = 144 with M = 124

What is the true mean for 1, 2, 3, 4, 5, and 6?

3.5

For samples selected from a population with μ = 90 and σ = 30, what sample size is necessary to make the standard distance between the sample mean and the population mean equal to 5 points? a. n = 6 b. n = 18 c. n = 36 d. n = 324

n = 36

You are interested in estimating the mean of a population. You plan to take a random sample from the population and use the sample's mean as an estimate mean. assume that the population from which your sample is not normal, which of the following statements about M are true? a. The expected value of M is equal to the value of the population mean. b. You can only assume that the sampling distribution of M is normally distributed for sufficiently large sample sizes. c. The sampling distribution of the z-score of M is normal for any sample size.

a and b

What is the z-score for a sample mean of M = 21 where the population mean is 24, the population standard deviation is 3, and the sample size is 16? a. 3 b. 2 c. -2 d. -4

-4

A beetle population has a mean length of 2.3 inches with standard deviation of 0.2 inches. What is the standard error for a sample size of 16? a. 0.0125 b. 0.05 c. 0.2 d. 0.8

0.05

find the standard error using the following: ~Population Mean= 7.06 ~Expected value of the M= 7.06 ~64 randomly selected students ~Standard Deviation= 1.610

0.201

A researcher is working with a population of data. He needs the standard distance between sample mean and the population mean to be at most 1.3. If the standard deviation of the population is 5, how large will the sample size need to be? a. 10 b. 11 c. 14 d. 15

15

A population has a mean of 120 and a standard deviation of 10. If a sample of size 25 is collected, how much distance on average is expected between the sample mean and the population mean? a. 10 b. 0.4 c. 2 d. It is impossible to tell.

2

The population of scores on a nationally standardized test forms a normal distribution with μ = 300 and σ = 50. If you take a random sample of n = 25 students, what is the probability that the sample mean will be less than M = 280? a. 2.28% b. 15.87% c. 84.13% d. 97.73%

2.28%

find the standard error using the following: ~Population Mean= 99.2 ~Sample M= 103.4 ~Random sample of 50 ~Standard Deviation= 21

2.97

For a normal population the sample mean M = 35 has the same z-score as the sample mean M = 43. What is the population mean? a. 4 b. 35 c. 39 d. 43

39

find the expected M using the following: ~Population Mean= 7.06 ~64 randomly selected students ~Standard Deviation= 1.610

7.06

If all the possible random samples of size n = 7 are selected from a population with μ = 70 and σ = 5 and the mean is computed for each sample, then what value will be obtained for the mean of all the sample means? a. 10 b. 70 c. 4900 d. Around 70 but probably not equal to 70

70

If the standard error among sample means is small, which of the following is true? I. All the possible sample means are clustered close together. II. A researcher can be confident that any individual sample mean will provide a reliable measure of the population. III. A researcher must be concerned that a different sample could produce a different conclusion. a. I only b. I and II c. I and III d. III only

I and II

Which of the following is a true statement for any population with mean μ and standard deviation σ? I. The distribution of sample means for sample size n will have a mean of μ. II. The distribution of sample means for sample size n will have a standard deviation of. III. The distribution of sample means will approach a normal distribution as n approaches infinity. a. I only b. III only c. I and II only d. I, II, and III

I, II, and III

What happens to the standard distance between the sample mean and the population mean when the sample size is multiplied by 4? a. It is divided by 2. b. It is doubled. c. It is divided by 4. d. It is multiplied by 4.

It is divided by 2.

All of the possible random samples of size 5 are selected from a population and the variance among these sample means is 16. If all possible random samples of size 10 are selected from the same population, what can we say about the variance of this new set of sample means? a. It will be exactly 16. b. It will be less than 16. c. It will be greater than 16. d. It will be exactly 32.

It will be less than 16.

The standard error for a particular sample is 3.6. A researcher needs the standard error to be 1.2. What should the researcher do to the sample size? a. Multiply the sample size by 9. b. Divide the sample size by 9. c. Multiply the sample size by 3. d. Divide the sample size by 3.

Multiply the sample size by 9.

Which of the following is not a characteristic of the distribution of sample means? a. The sample means should pile up around the population mean. b. The pile of sample means should tend to form a normal-shaped distribution. c. The sample means should have similar standard deviations as the population standard deviation. d. The larger the sample size, the closer the sample means should be to the population mean.

The sample means should have similar standard deviations as the population standard deviation.

True or False The mean of all possible samples is equal to the mean of the raw score population?

True

When computing z for a sample mean, which quantity is used? a. The standard error b. The population standard deviation c. Either the standard error or the population standard deviation would work. d. It depends on the population mean.

The standard error

Which quantity decreases as the sample size increases? a. The standard deviation b. The standard error c. The population mean d. The mean of all the sample means

The standard error

The brackets or error bars shown at the top of each bar extends__________ above and below each of the group means. a. one standard error b. one standard deviation

a

If a researcher is concerned that a standard error is too big for the sample mean to provide a reliable measure of the population mean, what can the researcher do? a. Increase the sample size. b. Decrease the sample size. c. Choose a different sample of the same size. d. There is nothing the researcher can do to help this problem.

Increase the sample size.

What is a sampling error? a. The natural error that exists between a sample and its corresponding population b. The error that results from potential incorrect measurement in the sample c. The error that results from rounding the measurements in a sample d. The error that results from samples not being random

The natural error that exists between a sample and its corresponding population