### Z-Scores, Standard Deviation, Sample Mean – Statistics

The key terms used in these STATS chapters include Sample Mean, Z-Scores,Standard Deviation, Population, Distribution, Median, Scale of Measurement, Ordinal Scale, Descriptive/Observational Research – STATS

A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?

M = 0 and s = 1

Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution?

##### X = 40

The box plot below depicts the median number of hours a population of N = 12 students reported studying for their first exam within a class. Which statement below is not true based on the box plot?

The interquartile range is 5.

For a sample with s = 9, a score of X = 67 corresponds to z = +1.00. What is the sample mean?

58

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. When the distribution is standardized, which value will be obtained for a score of X = 58 from the original distribution?

##### X = 55

For any distribution, what is the z-score corresponding to the median?

This is impossible to determine based on the information provided.

On an exam with µ = 52, a person has a score of X = 44. Which value for the standard deviation would give this person the highest position in the class distribution?

σ = 8

What is the shape of the distribution for the following set of data? Scores: 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5

Positively skewed

Analyzing historical records to measure behaviors that occurred in the past. What’s that called?

Archival research

Which research strategy would be used to figure out the average time per day that college students spend on their smartphones?

Descriptive

A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?

M = 0 and s = 1

Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution?

##### X = 40

The box plot below depicts the median number of hours a population of N = 12 students reported studying for their first exam within a class. Which statement below is not true based on the box plot?

The interquartile range is 5.

For a sample with s = 9, a score of X = 67 corresponds to z = +1.00. What is the sample mean?

58

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. When the distribution is standardized, which value will be obtained for a score of X = 58 from the original distribution?

##### X = 55

What’s the point of making a list of behaviors (behavioral categories) before starting an observational study?

To improve the reliability of the measurements

Although surveys can be used with a variety of different research strategies, the defining characteristic of the survey research design is that the ____.

Intent is simply to describe behaviors

What’s it called when you go back and forth between one minute of observation and one minute of writing down what you observed?

Time sampling

What’s the scale of measurement? elevation (feet above sea level)

What’s the scale of measurement? outcome of a horse race (1st, 2nd, 3rd)

Ordinal

What’s the scale of measurement? time of day (morning, afternoon, evening)

Ordinal

What’s the scale of measurement? time of day (1pm, 2pm, 3pm, etc.)

Interval

Which proportion of a normal distribution is located between z = 0 and z = +1.50?

0.4332

Intelligent quotient (IQ) scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQ scores above 140 are classified in the genius category. Which proportion of the population consists of geniuses?

#### 0.0038

A vertical line drawn through a normal distribution at z = -0.60 separates the distribution into two sections, the body and the tail. Which proportion of the distribution is in the body?

0.7257

What is the probability of randomly selecting a z-score greater than z = +1.25 from a normal distribution?

p = 0.1056

A population has SS = 100 and σ 2 = 5. How many scores are in the population?

##### 20

For a population with µ = 100 and σ = 20, what is the X value corresponding to z = -0.25?

X = 95

Under which circumstance is a score that is located 5 points above the mean a central value that is relatively close to the mean?

When the population standard deviation is much greater than 5

If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently _____ the population variance.

Underestimate

Consider a 100-point college exam for which there is a large number of students that perform extremely well, as well as a large number of students that perform extremely poorly. Which statement below is true?

The distribution of scores is probably bimodal.

What is the preferred measure of central tendency for scores measured on an ordinal scale?

The median

Bimodal distribution has

2 modes

For a data set that is skewed due to outliers, what is the most appropriate statistic of central tendency to use?

Median

Descriptive/Observational research

Studying individual variables simply in order to describe them (e.g., what % of students read feedback on Blackboard?)

Descriptive statistics

Numbers or figures that summarize a set of data from a sample

t

An inferential statistical test used to see if two sample means are more different than we’d expect due to chance

Noting the number of hours a week your sister spends playing video games is an example of the ____ method, while simply noting whether or not she played video games at all in a given week is an example of the ____ method.

##### Duration, interval

What are the three major categories of research methods?

Descriptive/observational, correlational, experimental

Identify the 2 variables in the following hypotheses, and suggest a way you could specifically measure each of them.
Are judges more lenient on attractive defendants?

The two variables in this hypothesis are “how lenient the judge is” and “how attractive the defendant is.” You could measure each of these by making surveys on the attractiveness of the defendants and keeping track of each defendants sentence (amount of community service, jail time, etc.), then comparing the results.

A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?

M = 0 and s = 1

Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution?

X = 40

The box plot below depicts the median number of hours a population of N = 12 students reported studying for their first exam within a class. Which statement below is not true based on the box plot?

The interquartile range is 5.

For a sample with s = 9, a score of X = 67 corresponds to z = +1.00. What is the sample mean?

##### 58

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. When the distribution is standardized, which value will be obtained for a score of X = 58 from the original distribution?

X = 55

What is the preferred measure of central tendency for scores measured on an ordinal scale?

The median

Bimodal distribution has

#### 2 modes

For a data set that is skewed due to outliers, what is the most appropriate statistic of central tendency to use?

Median

Descriptive/Observational research

Studying individual variables simply in order to describe them (e.g., what % of students read feedback on Blackboard?)

Descriptive statistics

Numbers or figures that summarize a set of data from a sample

t

An inferential statistical test used to see if two sample means are more different than we’d expect due to chance

Noting the number of hours a week your sister spends playing video games is an example of the ____ method, while simply noting whether or not she played video games at all in a given week is an example of the ____ method.

Duration, interval

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