Question 1

The precision with which a sample average approximates a population average increases as the ______ of the sample ________.
A) standard error; increases
B) normal distribution; increases
C) central tendency; increases
D) standard error; decreases

Accepted Answer

The precision of a sample average in approximating a population average increases as the standard error decreases, because a smaller standard error indicates that the sample mean is closer to the population mean.

Question 2

The symmetrical bell-shaped figure used to represent the frequency distribution of many physical and psychological characteristics is called a
A) histogram
B) normal curve
C) percentile rank
D) scatterplot

Accepted Answer

The normal curve is a symmetrical bell-shaped figure used to represent the frequency distribution of many physical and psychological characteristics.

Question 3

Many frequency distributions
A) precisely coincide with the normal curve
B) approximate the normal curve
C) define the normal curve
D) verify the normal curve

Accepted Answer

Many frequency distributions approximate the normal curve, meaning they have a similar bell-shaped distribution, but they do not precisely coincide with or define it.

Question 4

Approximately 68 percent of the cases represented by the normal curve fall within ________ standard deviation(s) from the mean.
A) 1
B) 2
C) 34
D) 68

Accepted Answer

Approximately 68 percent of the data in a normal distribution falls within one standard deviation from the mean.

Question 5

Approximately what percentage of the cases represented by the normal cure fall within 2 standard deviations from the mean?
A) 2
B) 4
C) 68
D) 95

Accepted Answer

Approximately 95% of the data in a normal distribution falls within 2 standard deviations from the mean.

Question 6

The control group mean
A) equals its population mean
B) equals the mean of its sampling distribution
C) probably has a value within a standard error of its population mean
D) probably has a value within a standard error of the experimental group mean

Accepted Answer

The answer of The control group mean
A) equals its population...

Question 7

If the null hypothesis is true, the standard error of the mean serves as a rough indicator of the average amount by which a control group mean would be expected to deviate from
A) its population mean
B) the experimental group mean
C) the mean of all the participants who participated in the experiment
D) all of the above

Accepted Answer

The answer of If the null hypothesis is true, the...

Question 8

Given that the population standard deviation equals 40 and that the sample consists of 25 observations, the standard error of the mean equals
A) 0.80
B) 1.60
C) 8.00
D) 40.00

Accepted Answer

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size: 40 / √25 = 40 / 5 = 8.00.

Question 9

According to the central limit theorem,
A) the standard deviation will always be smaller than the standard error
B) the standard deviation will always be larger than the standard error
C) the distribution of sample means will be normally distributed if your sample sizes are large enough
D) the distribution of sample means will be normally distributed if the underlying population is normally distributed

Accepted Answer

The central limit theorem states that the distribution of sample means will tend to be normally distributed, regardless of the shape of the population distribution, as long as the sample size is sufficiently large.

Question 10

Which of these terms is likely to be the smallest?
A) the standard deviation
B) the standard error
C) the standard error of the difference
D) the variance

Accepted Answer

The standard error is typically smaller than the standard deviation because it is the standard deviation divided by the square root of the sample size.

Question 11

You may be able to use an independent groups t test when
A) you have three or more groups
B) your observations are dependent
C) your scores are ordinal
D) your groups' variances are not equal

Accepted Answer

An independent groups t-test is used when comparing the means of two independent groups, assuming equal variances. If variances are not equal, a modified version called Welch's t-test can be used.

Question 12

The average of the experimental group is
A) equal to the control group mean, if the null hypothesis is true
B) greater than the control group mean, if the null hypothesis is true
C) probably within one standard error of the control group mean, if the null hypothesis is true
D) greater than the control group mean, if the null hypothesis is false

Accepted Answer

The answer of The average of the experimental group is
A)...

Question 13

In which case, would you be most likely to find a statistically significant effect?
A) the standard error of the difference is 1
B) the standard error of the difference is 5
C) the standard error of the difference is 10
D) the standard error of the difference is 50

Accepted Answer

A smaller standard error of the difference (1) indicates less variability in the estimate, making it more likely to detect a statistically significant effect if one exists.

Question 14

In which case will your standard error tend to be smallest?
A) your standard deviation is 1
B) your standard deviation is 5
C) your standard deviation is 10
D) your standard deviation is 50

Accepted Answer

The standard error is smallest when the standard deviation is smallest.

Question 15

In which case will your standard error tend to be smallest?
A) your sample size is 4
B) your sample size is 10
C) your sample size is 16
D) your sample size is 40

Accepted Answer

The standard error decreases as the sample size increases, so the largest sample size (40) will have the smallest standard error.

Question 16

If you have a normal distribution, 95% of the scores will be within ___ standard deviations of the mean.
A) 1
B) 2
C) 3
D) 4

Accepted Answer

In a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean, according to the empirical rule.

Question 17

If you have a normal distribution and a standard deviation of 2, 95% of the scores will be within ___ points of the mean.
A) 2
B) 4
C) 6
D) 8

Accepted Answer

95% of the scores will be within 1.96 standard deviations of the mean. So, 95% of the scores will be within 2 * 1.96 = 3.92 points of the mean.

Question 18

If the standard deviation is 100 and the sample size is 4, the standard error will be
A) 100
B) 50
C) 25
D) can't be determined from the information provided

Accepted Answer

The answer of If the standard deviation is 100 and...

Question 19

Standard deviation is to standard error as
A) range is to mean
B) range is to standard deviation
C) scores are to means
D) means are to scores

Accepted Answer

The answer of Standard deviation is to standard error as
A)...

Question 20

If scores in a distribution are not normally distributed, then
A) sample means will not be normally distributed
B) sample means will be normally distributed if the sample size is 30 or more
C) the sample means will be inaccurate
D) statistical significance will not be achieved

Accepted Answer

According to the Central Limit Theorem, the distribution of sample means will tend to be normal if the sample size is sufficiently large (usually n ≥ 30), regardless of the shape of the population distribution.

Quiz 16: Appendix E: Using Theory to Generate Research Hypotheses

The precision with which a sample average approximates a population average increases as the of the sample __.

The symmetrical bell-shaped figure used to represent the frequency distribution of many physical and psychological characteristics is called a

Many frequency distributions

Approximately 68 percent of the cases represented by the normal curve fall within ________ standard deviation(s) from the mean.

Approximately what percentage of the cases represented by the normal cure fall within 2 standard deviations from the mean?

The control group mean

If the null hypothesis is true, the standard error of the mean serves as a rough indicator of the average amount by which a control group mean would be expected to deviate from

Given that the population standard deviation equals 40 and that the sample consists of 25 observations, the standard error of the mean equals

According to the central limit theorem,

Which of these terms is likely to be the smallest?

You may be able to use an independent groups t test when

The average of the experimental group is

In which case, would you be most likely to find a statistically significant effect?

In which case will your standard error tend to be smallest?

In which case will your standard error tend to be smallest?

If you have a normal distribution, 95% of the scores will be within ___ standard deviations of the mean.

If you have a normal distribution and a standard deviation of 2, 95% of the scores will be within ___ points of the mean.

If the standard deviation is 100 and the sample size is 4, the standard error will be

Standard deviation is to standard error as

If scores in a distribution are not normally distributed, then