PSYC4700 2023 January Week 4 Assignment Latest

PSYC4700 Statistics for the Behavioral Sciences

Week 4 Assignment  

Probability

Complete the following problems within this Word document. (Do not submit other files.) Show your work for problem sets that require calculations. Ensure your answer to each problem is clearly visible. (You may want to highlight your answer or use a different font color to set it apart.)

Submit the document to your instructor by Sunday, 11:59 p.m. central time.

Problem Set 4.1: Probability and Conditional Probability

Criterion: Compute the probability.

Instructions: Read the following and answer the questions.

Researchers are often interested in the likelihood of sampling outcomes. They may ask questions about the likelihood that a person with a particular characteristic will be selected to participate in a study. In this exercise, we will select a sample of one participant from the following hypothetical student population of new and returning students living on or off campus. The population is summarized in the following table.

                New Student      Returning Student           Row Totals

On campus         30           25           55

Off campus         20           25           45

Column Totals    50           50           100

1.            What is the probability of selecting a new student participant?  _______________________¬¬¬¬

2.            What is the probability of selecting a returning student participant? ______________________

3.            What is the probability of selecting a student who lives on campus? _____________

4.            What is the probability of selecting a student who lives off campus? _____________

5.            What is the probability of selecting a new student, given that they live off campus? _______________________

6.            What is the probability of selecting a returning student, given that they live on campus? _______________________

                                                                                                                (Assignment continues on next page.)

7.            What is the probability of selecting a new student, given that they live on campus? ______________________

8.            What is the probability of selecting a returning student, given that they live off campus? _______________________

9.            What is the probability of selecting a student who lives on campus, given that they are a new student? _______________________

10.         What is the probability of selecting a student who lives off campus, given that they are a new student? _______________________

11.         What is the probability of selecting a student who lives on campus, given that they are a returning student? _______________________

12.         What is the probability of selecting a student who lives off campus, given that they are a returning student? _______________________

Problem Set 4.2: Determining Probability

Criterion: Determine the probability.

Instructions: Read the following and answer the question below.

Probability of first marriage among women. A National Center for Health Statistics (NCHS) brief report by the Centers for Disease Control and Prevention (CDC) in 2009 identified that about 6% of women in the United States married for the first time by their 18th birthday, 50% married by their 25th birthday, and 74% married by their 30th birthday.

Based on these data, what is the probability that in a family with two daughters, the first and second daughter will be married by each of the following ages?

1.            18 years of age:___________________________

2.            25 years of age:___________________________

3.            30 years of age:___________________________

Problem Set 4.3: Understanding Normal Distribution

Criterion: Solve problems with information about normal distributions and probabilities.

Instructions: Read the following and answer the questions.

Judging the humorousness of “lawyer” jokes. Stillman et al. (2008) conducted a study where participants listened to a variety of jokes. To determine how funny the jokes were, the researchers asked a group of 86 undergraduates to rate the jokes on a scale from 1 (very unfunny) to 21 (very funny). Participants rated a “lawyer joke” as one of the funniest jokes, with a rating of 14.48 ± 4.38 (M ± SD).

(Assignment continues on next page.)

Assuming that these data are normally distributed:

1.            What was the rating that marks the cutoff for the top 10% of participant ratings for this joke? ___________________________

2.            How many of the 86 undergraduates gave the joke a rating of at least 10? ___________________________

Problem Set 4.4: Calculating z Scores in JASP

Criterion: Calculate z scores using JASP.

Data: Use the Ratings data set. This data set is a record of how a sample of senior citizens rated the Internet on a 1–10 scale, with 1 being “really distrust it” and 10 being “completely trust it”:

Instructions: Complete the steps below.

1.            Download Ratings data set. Double-click the icon to open the data set in JASP.

2.            Just below the Toolbar, click the + sign next to the column labeled Rating.

3.            Type “Z scores” in the box, then click Create Column. A formula box will appear below the Toolbar.

4.            Use the scrollbar on the right side of the formula box to scroll down and select zScores(y).

5.            On the left side of the box, click Rating, then drag it into the formula box to replace the word values. Click Compute column at the bottom of the formula box.  You will see that the z scores have been added to the file. Paste a screenshot of the data set, showing the z scores, into the Word document.

6.            Answer: Which number of ratings is closest to the z score of 0?