Question 1

The difference between a normal distribution and a standard normal distribution is

Accepted Answer

A normal distribution can have any mean and standard deviation, while a standard normal distribution always has a mean of 0 and a standard deviation of 1.

Question 2

The difference between a standard score of -1.0 and a standard score of 1.0 is

Accepted Answer

Standard scores indicate how many standard deviations an observation is from the mean; a score of 1.0 is one standard deviation above the mean, and -1.0 is one standard deviation below the mean.

Question 3

If the test scores on an art history exam were normally distributed with a mean of 76 and standard deviation of 6, we would expect

Accepted Answer

In a normal distribution, scores are symmetrically distributed around the mean. Since 70 and 82 are both 6 points away from the mean of 76, we would expect almost equal numbers of students to score 70 and 82.

Question 4

Transforming a set of data to a new mean and standard deviation using a linear transformation

Accepted Answer

Transforming data to a new mean and standard deviation using a linear transformation is a common statistical practice, especially when comparing or combining data from different sources with different measurement scales. It does not alter the shape of the distribution and does not make the scores harder to work with, and in many cases is permissible.

Question 5

When we transform scores to a distribution that has a mean of 50 and a standard deviation of 10, those scores are called

Accepted Answer

Scores transformed into a distribution with a mean of 50 and standard deviation of 10 are referred to as T scores. Z scores have a mean of 0 and a standard deviation of 1, t scores are used in situations with smaller sample sizes and use a different formula, and stanine scores involve creating a distribution with nine equal intervals, each equivalent to half a standard deviation.

Question 6

Assume that your class took an exam last week and the mean and standard deviation of the exam were 85 and 5, respectively. Your instructor told you that 30 percent of the students had a score of 90 or above. You would probably

Accepted Answer

If the normal distribution is assumed, we can use the z-score formula to find the proportion of students who scored 90 or above. However, if the actual proportion is significantly different from the expected proportion based on the normal distribution, it suggests that the distribution is not normal. Therefore, it is more likely that the scores were not normally distributed and the assumption of normality should be checked. Without further information on the distribution, we cannot draw any conclusions about individual scores.

Question 7

The normal distribution is often referred to as the bell curve.

Accepted Answer

The normal distribution is commonly referred to as the bell curve due to its characteristic shape resembling a bell.

Question 8

In a normal distribution, about how much of the distribution lies within two (2) standard deviations of the mean?

Accepted Answer

According to the empirical rule, about 95% of the data will lie within two standard deviations of the mean in a normal distribution.

Question 9

The most common situation in statistical procedures is to assume that

Accepted Answer

The most common assumption made in statistical procedures is that the data are normally distributed. This assumption allows for the application of many statistical tests and procedures that rely on the assumption of normality. While it is possible for data to be skewed in either direction, normality is the most commonly assumed distribution in statistical analysis.

Question 10

Stanine scores

Accepted Answer

Stanine scores have a mean of 5 and vary between 1 and 9, making them similar to a standard normal distribution. Additionally, stanine scores are always integers, which are a whole number and not a fraction or decimal. Therefore, both options B and C are correct. Option A is incorrect as there is no indication that stanine scores are skewed in any way.

Question 11

If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately

Accepted Answer

The 95% confidence interval for a normally distributed dataset is calculated as the mean plus or minus 1.96 times the standard deviation. In this case, with a mean of 50 and a standard deviation of 10, the interval is 50 ± (1.96*10), which roughly equals 30 to 70.

Question 12

Which of the following is NOT always true of a normal distribution?

Accepted Answer

A normal distribution does not necessarily have a mean of 0, but it does have a symmetric bell-shaped curve and is unimodal. However, the mean of a normal distribution can be any value.

Question 13

We are interested in what the text calls "probable limits" because

Accepted Answer

The text states that probable limits can be used to identify whether data is unusual (A), to have a good idea of what kind of values to expect (B), and to determine if certain values are improbable (C). Therefore, all of the above options are valid reasons for being interested in probable limits.

Question 14

"Abscissa" is to _______ as "ordinate" is to _______.

Accepted Answer

"Abscissa" refers to the horizontal axis in a graph, while "ordinate" refers to the vertical axis. Therefore, the best choice is C: horizontal; vertical. Choices A and B are incorrect because they refer to statistical concepts that are not related to graphing. Choice D is incorrect because it has the opposite order of the correct relationship between absicssa and ordinate.

Question 15

An example of a linear transformation is

Accepted Answer

A linear transformation is a mathematical operation that follows the rules of linear algebra, which means that it involves only simple arithmetic operations such as addition, subtraction, and multiplication by a constant. Converting heights from feet to meters involves multiplying by a constant (0.3048), which is a linear transformation. Similarly, subtracting the value of the mean from each individual IQ score and dividing by the value of the standard deviation involves subtracting a constant and dividing by a constant, which are both linear transformations. Therefore, both options A and B are examples of linear transformations.

Question 16

For a normal distribution

Accepted Answer

Option A is incorrect as not all of the data points lie within one standard deviation from the mean in a normal distribution.
Option B is correct as about 2/3 of the distribution lies within one standard deviation from the mean in a normal distribution.
Option C is also correct as about 95% of the distribution lies within two standard deviations from the mean in a normal distribution. Therefore, both options B and C are correct, making option D the best choice.

Question 17

The difference between "probable limits" and "confidence limits" is that the probable limits

Accepted Answer

The answer of The difference between "probable limits" and "confidence...

Question 18

The advantage of using T-scores and standard scores is

Accepted Answer

T-scores and standard scores provide a common form of reference to everyone using them, which allows for easy comparison and interpretation of scores across different groups or individuals. This is particularly important in fields such as psychology or education where standardized assessments are commonly used. Choices B, C, and D are not accurate statements about T-scores and standard scores.

Question 19

A normal distribution

Accepted Answer

A normal distribution is symmetrical, meaning that it has an equal number of data points to the left and right of the mean. Option A and B are not true for a normal distribution, while option C is only true for a specific normal distribution with a certain standard deviation.

Question 20

A test score of 84 was transformed into a standard score of -1.5. If the standard deviation of test scores was 4, what is the mean of the test scores?

Accepted Answer

The answer of A test score of 84 was transformed...

Quiz 6: The Normal Distribution