Statistics Midterm Study Guide

For a population with m = 80 and s = 10, what is the z-score corresponding to X = 85?

+0.50

For a population with s = 4, an individual with a deviation score of +2 would have a z-score of ____.

+0.50

For a population with m = 80 and s = 10, what is the z-score corresponding to X = 70?

-1.00

If a population with m = 60 and s = 8 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of ____ and a standard deviation of ____.

0 and 1

What is the variance for the following population of scores? Scores: 5, 2, 5, 4

1.5

What is the value of Σ(X - 1)2 for the scores 1, 2, 1, 4?

10

What is the value of Σ(X - 2)2 for the scores 2, 3, 5?

10

A population of scores has m = 50 and s = 12. If you subtract five points from every score in the population, then the value for the new standard deviation will be ____.

12

In a population of N = 10 scores, the smallest score is X = 8 and the largest score is X = 20. The range for the population is ____.

13

A sample of n = 5 scores has M = 20 and s2 = 4. What is the sample standard deviation?

2

In a correlational study,

2 variables are measured and there is only 1 group of participants.

What is the value of ΣX2 for the scores 1, 0, 2, 4?

21

A population of N = 10 scores has m = 50 and s = 5. What is the population variance?

25

For the following frequency distribution of exam scores, how many students had scores lower than X = 80? X f 90-94 3 85-89 4 80-84 5 75-79 2 70-74 1

3

For the population of scores shown in the frequency distribution table, the mean is Xf 52 41 34 23 12

34/12 = 2.83

For the population of scores shown in the frequency distribution table, the mean is Xf 52 41 34 23 12

34/12 = 2.83

A population has m = 40 and s = 8. If each score is divided by 2, the new standard deviation will be ____.

4

In a population with m = 60, a score of X = 58 corresponds to a z-score of z = -0.50. What is the population standard deviation?

4

What is the value of Σ(X - 2) for the scores 2, 3, 5?

4

A population of N = 5 scores has SS = 40. What is the variance for this population?

40/5 = 8

A set of score has a mean of m = 63 and a standard deviation of s = 8. If these scores are standardized so that the new distribution has m = 50 and s = 10, what new value would be obtained for a score of X = 59 from the original distribution?

45

What is the median for the following set of scores? Scores: 1, 4, 6, 17

5

What is the median for the following set of scores?Scores: 1, 4, 6, 17

5

​A set of scores ranges from a high of X = 72 to a low of X = 28. If these scores were put in a grouped frequency distribution table, what would be the best choice for the interval width?

5 points​

A sample of n = 5 scores has a mean of M = 9. What is SX for this sample?

5(9) = 45

What is the value of the median for the following set of scores? Scores: 1, 3, 3, 5, 6, 7, 8, 23

5.5

What is the value of the median for the following set of scores?Scores: 1, 3, 3, 5, 6, 7, 8, 23

5.5

For a population with m = 60 and s = 8, what is the X value corresponding to z = -0.50?

56

For a population with m = 60 and s = 8, what is the X value corresponding to z = 1.50?

72

A population of scores has s = 20. In this population, a score of X = 80 corresponds to z = +0.25. What is the population mean?

75

What is the value of ΣX + 1 for the scores 1, 0, 2, 4?

8

For a population with μ = 100 and σ = 20, what is the X value corresponding to z = -0.75?​

85

What is the first step to be performed when computing Σ(X + 2)2?

Add 2 points to each score

A recent study found a correlation between gum disease and heart disease. This result indicates that gum disease causes people to develop heart disease.​

False

A researcher interested in vocabulary development obtains a sample of 3-year-old children to participate in a research study. The average score for the group of children is an example of a parameter.​

False

A set of scores ranges from X = 18 to X = 91. If the scores were put in a grouped frequency distribution table with an interval width of 10 points, the top interval would be 91-100.​

False

For the following distribution of scores, 20% of the individuals have scores of X = 1. X f 5 2 4 8 3 5 2 3 1 2

False

For the following scores, SX2 = (SX)2. Scores: 1, 1, 1, 1​

False

For the following scores, ΣX2 = 49. Scores: 1, 4, 2, 0

False

If a set of exam scores forms a negatively skewed distribution, it suggests that the majority of the students did not score well on the exam.

False

In February in New York, the daily high temperatures are typically low with only a few relatively warm days. A frequency distribution showing the daily high temperatures would probably form a negatively skewed distribution.​

False

In a grouped frequency distribution table, the top value in each class interval should be a multiple of the interval width.​

False

For statistical purposes, it usually is not important to differentiate between which two scales of measurement?

Interval and ratio

Students in an introductory art class are classified as art majors and non-art majors. What scale of measurement is being used to classify the students?

Nominal

What term is used to describe the shape of a distribution in which the scores pile up on the left-hand side of the graph and taper off to the right?​

Positively skewed

The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshmen and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept is used to explain the natural difference that exists between a sample mean and the corresponding population mean?

Sampling error

What is the first step to be performed in the following mathematical expression, ΣX2?

Square each score

In general, what is the relationship between the standard deviation and variance?

Standard deviation is the square root of variance.

What is the final step to be performed when computing Σ(X - 2)2?

Sum the squared values

A sample of n = 40 scores has a mean of M = 75. If one new score with a value of X = 90 is added to the sample, what will happen to the sample mean?

The mean will increase.

A sample has a mean of M = 30. If one score with a value of X = 10 is removed from the sample, what effect will it have on the sample mean?

The sample mean will increase

A sample has a mean of M = 25. If a new score with a value of X = 25 is added to the sample, what effect will it have on the sample mean?

The sample mean will remain the same.

What additional information is obtained by measuring two individuals on an interval scale compared to an ordinal scale?

The size of the difference

Last week, Bob had a score of X = 45 on a mathematics exam and a score of X = 61 on an English exam. If the math exam scores had a mean of m = 40 with s = 5, and the English exam scores had a mean of m = 51 with s = 10, for which exam should Bob expect the better grade?

The two exam scores are in equivalent locations so Bob should expect the same grade in both classes.

A researcher is interested in the average income for registered voters in the United States. The entire group of registered voters is an example of a population.​

True

For statistical purposes, there usually is not much reason to differentiate between interval and ratio scales.​

True

For the following distribution of scores, SX = 18. X f 4 1 3 2 2 3 1 2

True

For the following scores, Σ(X + 1) = 9. Scores: 1, 3, 0, 1

True

If a distribution with more than 15 or 20 possible scores is being organized in a frequency distribution table, a grouped table should be used.​

True

It is customary to list the score categories in a frequency distribution from the highest down to the lowest.

True

The first step in computing Σ(X + 1) is to add 1 point to each score.​

True

Using the election results from a sample of n = 100 voters to predict the results for the entire state is an example of inferential statistics.​

True

​The normal distribution is an example of a symmetrical distribution.

True

For a population with m = 100 and s = 20, the X value corresponding to z = 1.50 is

X = 130

The median for any distribution corresponds to a z score of ____.

cannot be determined from the information given

For a perfectly symmetrical distribution with m = 30, the median would have a value ____.

equal to 30

In N = 25 games last season, the college basketball team averaged m = 74 points with a standard deviation of s = 6. In their final game of the season, the team scored 90 points. Based on this information, the number of points scored in the final game was ____.

far above average

One sample of n = 4 scores has a mean of M = 10, and a second sample of n = 8 scores has a mean of M = 20. If the two samples are combined, the mean for the combined sample will be

greater than 15 but less than 20

A population of scores has m = 50 and s = 10. If every score in the population is multiplied by 2, then the new mean and standard deviation would be

m = 100 and s = 20

Suppose you earned a score of X = 54 on an exam. Which set of parameters would give you the highest grade?

m = 50 and s = 2

In a positively skewed distribution, which measure of central tendency will have the largest value?

mean

Which of the following is true for a symmetrical distribution?

mean = median

A distribution can have more than one ____.

mode

For any distribution, you can be sure that at least one individual has a score equal to the ____.

mode

Degrees of freedom for sample variance are determined by ____.

n - 1

To compute sample variance, the value of SS is divided by ____.

n - 1

If a distribution of scores is shown in a bar graph, you know that the scores were measured on a(n) _________ scale of measurement.​

nominal or ordinal

Determining the class standing (1st, 2nd, and so on) for the graduating seniors at a high school would involve measurement on a(n) _____ scale of measurement.

ordinal

A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. The goal of the research is to determine the average number of hours each day that American adolescents spend watching television. The researcher is trying to determine a number that is an example of a _____.

parameter

Define the concept of "sampling error." Note: your definition should include the concepts of sample, population, statistic, and parameter.

sampling error is the measure of the difference between a set of statistic samples. this measure in difference is used to identify the population parameter.

The variability of the scores in a sample tends to be ____ the variability of the scores in the population from which the sample was obtained.

smaller than

The symbol SS stands for the ____.

sum of squared deviations

For an experiment comparing two methods of teaching social skills training to autistic children, the independent variable is _______ and the dependent variable is _______.

teaching methods; the social skills that are learned

The most commonly used measure of central tendency is ____.

the mean

A researcher is measuring problem-solving times for a sample of n = 20 children. However, one of the children fails to solve the problem so the researcher has an undetermined score. What is the best measure of central tendency for these data?

the median

For an extremely skewed distribution of scores, the best measure of central tendency would be ____.

the median

The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that ____.

the population mean is between 5 and 10, and the standard deviation is less than 6

Under what circumstances would a score that is 15 points above the mean be considered an extreme score?

when the population standard deviation is much smaller than 15

You are instructed to subtract 4 points from each score, square the resulting value, and find the sum of the squared numbers. How would this set of instructions be expressed in summation notation?

Σ(X - 4)2

​In a grouped frequency distribution, one interval is listed as 50-59. Assuming that the scores are measuring a continuous variable, what are the real limits for this interval?

​49.5 and 59.5

What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?​

​A bar graph

A researcher surveys a sample of n = 200 college students and asks each person to identify his or her favorite movie from the past year. If the data were organized in a frequency distribution table, what would be listed in the first column?​

​A list of movies

If a set of exam scores forms a symmetrical distribution, what can you likely conclude about the students' scores?​

​About an equal number of students had relatively high and relatively low scores.

For the following distribution, how many people had scores less than X = 19? X f 20-24 2 15-19 5 10-14 4 5-9 1

​Cannot be determined

For the following frequency distribution of exam scores, what is the lowest score on the exam? X f 90-94 3 85-89 4 80-84 5 75-79 2 70-74 1

​Cannot be determined

A researcher collects a sample of n = 20 Introductory Psychology textbooks and records the number of pages in each book. The results are then placed in a grouped frequency distribution table using intervals of 0-99 pages, 100-199 pages, 200-299 pages, and so on. If the results were converted into a frequency distribution graph, what kind of graph should be used​

​Either a histogram or a polygon

What is the shape of the distribution for the following set of data? Scores: 1, 2, 3, 3, 4, 4, 4 5, 5, 5, 5, 6​

​Negatively skewed

If a set of scores is displayed in a frequency distribution bar graph, what scale of measurement was used to measure the scores?​

​Nominal or ordinal

In a distribution with positive skew, scores with the highest frequencies are _____.​

​on the left side of the distribution