course: just 3900 introductory statistics for criminal justice test review: ch. 1-3 peer tutor...

COURSE: JUST 3900INTRODUCTORY STATISTICS

FOR CRIMINAL JUSTICETest Review: Ch. 1-3

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Chapter 1: Intro to Stats

Question 1: A psychology professor is interested in the tweeting habits of college freshman at ECU. If the professor measures the number of tweets that each freshman in her classes sends each day and calculates the average number for all of her classes, the average number would be an example of a ________.


Question 1 Answer: The average would be an example of a statistic because the

professor conducted her research using a sample (the freshman in her classes, not the entire freshman class at ECU).


Question 2: A researcher wants to know the relationship between gender and cell phone preference. He uses surveys asking men and women which they prefer: texting or calling. Is this an example of an experiment? Why or why not?


Question 2 Answer: This would not be an example of an experiment because the

researcher did not manipulate any variables; he simply observed the difference between the cell phone usage of men and women. This study would be correlational or nonexperimental.


Question 3: Suppose a researcher wanted to know the relationship between cell phone preference (texting or calling) and type of phone (flip phone or smart phone). To accomplish this he designs an experiment in which there are 2 groups. One group is issued iphones, while the other is issued flip phones. The researcher then records every call and text for a month to determine whether the type of phone influences cell phone preference. Identify the independent and dependent variables for this study.


Question 3 Answer: The independent variable is the type of phone. This is the

variable that the researcher is manipulating; it affects the outcome of the dependent variable.

The dependent variable is cell phone preference. We expect the independent variable (type of phone) to have an effect on the dependent variable (cell phone preference).


Question 4: A survey asks students to identify their gender, age, and GPA. For each of these three variables, identify the scale of measurement that probably is used and identify whether the variable is discrete of continuous.


Question 4 Answer: Gender is measured on a nominal scale and is discrete. Age

and GPA are measured on ratio scales and are both continuous variables.


Question 5: When measuring weight to the nearest half pounds, what are the real limits for a score of 150 lbs?

Hint: The question wording here is slightly different than the way real limits are discussed in class, but the approach to calculating real limits is the same. In class, weight was discussed as being measured in whole pounds and real limits are calculated based upon half intervals above and below any given point in the weight scale. Thus, the real limits for a score of 150 pounds measured in whole pounds would be 145.5 to 150.5 (this is how you did this in class). Question #5 as written above in this slide indicates that weight was measured to the nearest half pound. This changes the calculation of real limits. Try to answer this yourself and then review the answer on the next slide to see if you answered this correctly.


Question 5 Answer: URL 150.25 LRL 149.75

149.5 150 150.5

149.75 150.25


Question 6: Calculate for the following scores: 5, 4, 3, 2, 1


Question 6 Answer:

Exponents before summation.


Question 7: Use summation notation to express the following: Subtract 10 points from each score, square them and then add the resulting values.


Question 9 Answer:

Chapter 2: Frequency Distributions

Question 1: Make a stem and leaf plot using the following set of N = 20 scores: 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18,

14, 11


Question 1 Answer: 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18,

14, 11

Stem Leaf

0 8996

1 46036205741841

2 72


Question 2: If you were asked to create a grouped frequency table using the following set of N = 25 scores, how many intervals would you have and what would their width be? 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84,

70, 76, 89, 75, 80, 73, 78, 60


Question 2 Answer: We want 9 intervals with a width of 5. Remember the guidelines on pp. 42 and 43. For a grouped

frequency distribution, we want about 10 intervals. Also, we want our interval width to be a simple number.

A width of 2 gives us 21 rows (too many) A width of 5 gives us 9 rows (OK) A width of 10 gives us 5 rows (too few)


Question 3: What are the differences between histograms and a bar graphs?


Question 3 Answer: Histograms are used for interval and ratio data, while bar graphs

are used for nominal or ordinal data. Bar graphs have space between the bars because they

represent discrete variables. Histograms have no space between the bars because they

represent continuous variables.


Question 4: Label each frequency distribution as symmetrical, positively skewed or negatively skewed.


Question 4 Answer:

Positively Skewed Negatively Skewed

Symmetrical Symmetrical


Question 5: Find the 80th percentile.


Question 5 Answer: Step 1: Find the width of the interval on both scales

5 and 25 points, respectively Step 2: Locate position of intermediate value

80% is located 15 points from top (15/25 = 3/5 of interval) Step 3: Use same fraction to determine corresponding position

on other scale. First, determine the distance from the top of the interval

Distance = Fraction x Width = (3/5) * (5 points) = 3 Points Step 4: Use distance from top to determine the position on the

other scale 19.5 – 3 = 16.5 Thus, the 80th percentile for X is 16.5.

Chapter 3: Central Tendency

Question 1: A sample of scores has a mean of . What is the value of for this sample?


Question 1 Answer:


Question 2: A sample of scores has a mean of . One new score is added to the sample and the new mean is found to be . What can you conclude about the value of the new score? Greater than 50. Less than 50. Need more information.


Question 2 Answer: The new score must be greater than 50.


Question 3: One sample has scores with a mean of . A second sample has a mean of scores with a mean of . If the two samples are combined, what is the mean for the combined sample?


Question 3 Answer:


Question 4: A population has a mean of .a) If 5 points were added to every score, what would be the value

for the new mean?

b) If every score were multiplied by 5, what would be the value for the new mean?


Question 4 Answer:a) The new mean would be 55.

b) The new mean would be 250.


Question 5: Find the median for the distribution of scores: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5


Question 5 Answer: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 Median: 4

Because:


Question 6: The following is a distribution of measurements for a continuous variable. Find the precise median that divides the distribution exactly in half. 1, 2, 2, 3, 4, 4, 4, 4, 4, 5


Question 6 Answer: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5

Median: 3.70 (one-fifth of the way into the interval from 3.5 to 4.5).

1 2

3

4 1

1 2 3 4 5

1/5 4/5


Question 7: What is the mode of the following distribution?


Question 7 Answer: The distribution is bimodal. The major mode is . The minor mode is .


Question 8: Which measure of central tendency is most affected if one extremely large score is added to a distribution (mean, median, mode)?


Question 8 Answer: Mean.

Notice that the mean follows the extreme scores.


Question 9: Why is it usually considered inappropriate to compute a mean for scores measured on an ordinal scale?


Question 9 Answer: The definition of the mean is based on distances and ordinal

scales do not measure distance.


Question 10: In a perfectly symmetrical distribution, the mean, the median, and the mode will all have the same value. (True or False?)


Question 10 Answer: False, if the distribution is bimodal.


Question 11: A distribution with a mean of 70 and a median of 75 is probably positively skewed. (True or False?)


Question 11 Answer: False. The mean is displaced toward the tail on the left-hand

side.

7075

course: just 3900 introductory statistics for criminal justice test review: ch. 1-3 peer tutor...

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type of phone flip phone

smart phone

cell phone preference

stats question

cell phone usage of

average number

entire freshman class

psychology professor