Question 1

Gerber and Malhotra (2006) found a suspiciously low number of z scores just outside of the cutoff for significance, indicating that researchers might be encouraged to "beat" the cutoff for significance.

Accepted Answer

Gerber and Malhotra (2006) found evidence to support the idea that researchers may be motivated to "beat" the cutoff for statistical significance, which could result in the suppression or exaggeration of results.

Question 2

The standard deviation of a distribution of sample means is smaller than the standard deviation of the population when the sample size is 2.

Accepted Answer

This statement is false. The standard deviation of a distribution of sample means will decrease as the sample size increases, not just when the sample size is 2. This is known as the central limit theorem.

Question 3

A z score of -1.0 represents _____ a z score of -3.0.

Accepted Answer

A z score of -1.0 is closer to the mean than a z score of -3.0, indicating a higher score.

Question 4

A distribution has a mean of 1.57 with a standard deviation of 0.24.A z score of -0.62 converts into a raw score of _____, whereas a z score of 0.62 converts into a raw score of _____.

Accepted Answer

The formula to convert a z-score to a raw score is X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the z-score. For a z-score of -0.62: X = 1.57 + (-0.62)(0.24) = 1.42. For a z-score of 0.62: X = 1.57 + (0.62)(0.24) = 1.72.

Question 5

Approximately _____ percent of scores fall between the mean and a z score of -2.

Accepted Answer

The answer of Approximately _____ percent of scores fall between...

Question 6

The standard deviation of a distribution of means will be larger than the standard deviation of a distribution of scores.

Accepted Answer

The standard deviation of a distribution of means, often referred to as the standard error, is typically smaller than the standard deviation of the distribution of individual scores because it reflects the variability of sample means around the population mean, which decreases as sample size increases.

Question 7

Standard error is the variance of a distribution of means.

Accepted Answer

Standard error is the standard deviation of a distribution of means, not the variance.

Question 8

A(n) _____ is the number of standard deviations a score is from the mean.

Accepted Answer

The z score is a measure of standard deviation from the mean, calculated by subtracting the mean from the raw score and dividing the result by the standard deviation. It is expressed in terms of the number of standard deviations above or below the mean.

Question 9

The distribution of means is less variable than the distribution of scores.

Accepted Answer

This is because the distribution of means is affected by the sample size and tends to become more normal with larger sample sizes (Central Limit Theorem). In contrast, the distribution of scores can have more extreme values and outliers.

Question 10

Approximately _____ percent of scores fall within 1 standard deviation from the mean.

Accepted Answer

According to the empirical rule, approximately 68% of scores fall within 1 standard deviation from the mean. This means that if we have a normal distribution, 68% of the scores would fall between (mean - standard deviation) and (mean + standard deviation).

Question 11

Standard error is the standard deviation of a distribution of means.

Accepted Answer

This statement is true. The standard error is calculated by dividing the standard deviation of a distribution by the square root of the sample size. It provides an estimate of the uncertainty of the sample mean and is used to make inferences about the population mean.

Question 12

A z score of -2.0 represents _____ a z score of 1.0.

Accepted Answer

A z score of -2.0 is 2 standard deviations below the mean, while a z score of 1.0 is only 1 standard deviation above the mean. Therefore, a z score of -2.0 represents a lower score than a z score of 1.0.

Question 13

Approximately _____ percent of scores fall between the mean and a z score of 1.

Accepted Answer

According to the empirical rule, approximately 34% of scores fall between the mean and a z score of 1. This is because 68% of scores fall within one standard deviation of the mean, and half of that (34%) falls between the mean and a z score of 1.

Question 14

The process of standardization converts individual scores from different distributions to a shared distribution with a known:

Accepted Answer

The answer of The process of standardization converts individual scores...

Question 15

A z score computed for a sample mean is called a z statistic.

Accepted Answer

This statement is true. A z score calculated for a sample mean is referred to as a z statistic.

Question 16

Approximately _____ percent of scores fall between the mean and a z score of -1.

Accepted Answer

Approximately 34 percent of scores fall between the mean and one standard deviation below the mean (a z score of -1) in a normal distribution.

Question 17

A z score of 0 is equivalent to the:

Accepted Answer

A z score of 0 indicates that the data point is equal to the mean, so the correct choice is the mean (B). A z score of 1 would be one standard deviation above the mean, and a z score of -1 would be one standard deviation below the mean. Standard deviation (A), standard error (C), and variance (D) are not equivalent to a z score of 0.

Question 18

Approximately _____ percent of scores fall between the mean and a z score of 2.

Accepted Answer

Approximately 48 percent of scores fall between the mean and a z score of 2 in a standard normal distribution, as the area between the mean and a z score of 2 is about 0.4772, which is roughly 48 percent.

Question 19

A distribution has a mean of 600 with a standard deviation of 50.A z score of 2.04 converts into a raw score of:

Accepted Answer

A z-score is calculated as (X - mean) / standard deviation. Rearranging gives X = (z-score * standard deviation) + mean. Substituting the given values: X = (2.04 * 50) + 600 = 702.00.

Question 20

A z score allows assessment of the percentile of a raw score, but an equivalent assessment of a sample mean cannot be made.

Accepted Answer

A z score can also be used to assess the percentile of a sample mean in a distribution of sample means, often referred to as the sampling distribution of the mean, by standardizing the sample mean in a similar manner to individual scores.

Quiz 6: The Normal Curve, Standardization and Z Scores