Ch. 6

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean?

.0228

A researcher selects a sample of 64 participants from a population with a mean of 10 and a variance of 16. What is the standard error of the mean?

0.5

A researcher selects a sample of size 6 from a population of size 10. How many possible samples of this size can be selected using theoretical sampling?

1,000,000

A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling?

15

A researcher selects a sample of 121 participants from a population with a mean of 32 and a standard deviation of 22. What is the standard error of the mean?

2.0

Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means?

the central limit theorem

Experimental research is typically conducted using a sampling strategy in which ______.

the same participant can never be selected twice in the same sample

How is the standard error of the mean typically reported in a graph?

using error bars

A researcher selects two samples of 25 participants each. In the first sample, the population mean was 32 and the variance was 8. In this second sample, the population mean was 4 and the variance was 8. Which sample will be associated with a larger standard error of the mean?

None, both samples will have the same value for standard error

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 18, mc025-1.jpg = 8, mc025-2.jpg = 2.4 Researcher B: n = 12, mc025-3.jpg = 8, mc025-4.jpg = 2.4

Researcher A

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 36, mc024-1.jpg = 12, mc024-2.jpg = 9 Researcher B: n = 36, mc024-3.jpg = 12, mc024-4.jpg = 6

Researcher B

Two researchers select a sample for a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants. Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error?

Researcher B's, because the sample size was larger.

A researcher selects two samples of 64 participants each. In the first sample, the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean?

Sample 1

A researcher randomly selects a sample of athletes and reports that their average score on a health and fitness scale is 23. Based on the characteristics of the sample mean, what does this say about the mean in the population?

We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean.

A sampling distribution of the sample mean or variance is ______.

a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population

The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n - 1) ______.

are both unbiased estimators

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean equal to at least 12?

equal to the probability of selecting a sample mean that is at most equal to 8

Which type of sampling is most often applied by researchers in the behavioral sciences?

experimental sampling

Each of the following statements are true, except that ______.

the larger the sample size, the larger the standard error

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called ______.

a sampling distribution

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean of 13 or larger from this population?

less than .03

A researcher randomly selects a sample of participants from a population with a variance of 4. If a researcher selects a sample of 16 participants with a mean of 12, then what is the mean and standard error for the sampling distribution of the mean?

mean = 12, standard error = 0.5

The shape of the sampling distribution of the mean is approximately ______, whereas the shape of the sampling distribution of the variance is approximately ______

normal; positively skewed

Suppose you select a sample of three people from a population of four (A, B, C, D). Which of the following samples is possible using the experimental sampling strategy?

persons B, C, and D

What does it mean to say that the sample mean is an unbiased estimator of the population mean?

If we select a sample at random, then on average we can expect the sample mean to equal the population mean.

What is the central limit theorem?

It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population

An article states that a sample of 40 participants took 12 ± 2.3 (M ± SEM) s to complete a cognitive assessment. Which value is the standard error of the mean?

2.3

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of ______.

36 and 40

A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM) dollars on groceries each week. Which value is the standard error of the mean?

40

A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3. About 14% of the sample means in this sampling distribution should be between a sample mean of ______.

9 and 10

Because the sampling distribution of sample means is normally distributed, we can use the z transformation formula to find probabilities. Which of the following gives the appropriate notation for this formula?

all of these

In terms of characterizing samples, statistical theory was developed using a sampling strategy in which ______.

all of these (the order of selecting participants matters, the same participant can be selected twice in the same sample, participants are replaced after being sampled)

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at least equal to the population mean?

both A and B

It happens to be the case that the standard error of the sampling distribution of sample means ______.

both A and C

Regardless of the distribution of the population, the sampling distribution of sample means will be approximately normally distributed. What characteristic of the mean explains this?

central limit theorem

A researcher increases the sample size, which will ______.

decrease the value of standard error

As sample size increases, the standard error of the mean ______.

decreases

The mean of the sampling distribution of sample means is ______.

equal to the population mean

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 25, mc026-1.jpg = 5, mc026-2.jpg = 7 Researcher B: n = 25, mc026-3.jpg = 32, mc026-4.jpg = 7

They both have the same standard error.

What values are distributed along the x-axis for a sampling distribution of the sample mean?

sample means

What values are distributed along the x-axis for a sampling distribution of the sample variance?

sample variances

A researcher selects from a participant pool of four males and six females. He determines that the probability of selecting two male participants is p = .16. Based on this probability, what strategy did the researcher use to sample participants?

sampling with replacement

A researcher selects from a participant pool of four males and six females. He determines that the probability of selecting two female participants is p = .30. Based on this probability, what strategy did the researcher use to sample participants?

sampling without replacement