Problem Set 2.1 Characteristics of the Mean

Assessment 2 – Central Tendency and Probability

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

Problem Set 2.1: Characteristics of the Mean

Criterion: Describe a distribution.

Instructions: Read the following and answer the questions.

Data: To study perception, a researcher selects a sample of participants (n = 12) and asks them to hold pairs of objects differing in weight, but not in size, one in each hand. The researcher asks participants to report when they notice a difference in the weight of the two objects. Below is a list of the difference in weight (in pounds) when participants first noticed a difference. Answer the following questions based on the data given in the table.

 

Difference in Weight
4 8
9 5
12 7
6 15
10 4
8 8

 

  1. State the following values for this set of data:
  1. Mean _______
  2. Median _______
  3. Mode(s) _______

 

  1. What is the shape of this distribution? Hint: Use the values of the mean, median, and mode to infer the shape of this distribution. __________________________

Problem Set 2.2.a: Interpret Means in a Chart

Criterion: Interpret means in a chart.

Instructions: Read the information below and answer the questions.

Data: General life satisfaction across culture. Gilman and colleagues (2008) measured general life satisfaction in 1,338 adolescents from two individualistic nations (Ireland, United States) and two collectivist nations (China, South Korea) using the Multidimensional Students’ Life Satisfaction Scale (MSLSS). Mean participant scores on the MSLSS are given in the following table.

 

Mean MSLSS Scores by Nation and Gender  
Nation Gender  
 

 

 

Men Women  
United States 4.39 4.61  
Ireland 4.37 4.64
China 4.41 4.56
South Korea 3.92 3.78

 

  1. Among which group was general life satisfaction lowest on average? __________________________
  2. Among which group was general life satisfaction highest on average? __________________________

Problem Set 2.2.b: Understanding Standard Deviations in a Chart

Criterion: Interpret standard deviations in a chart.

Instructions: Read the following and answer the question based on the data in the chart.

Data: Acceptable height preferences. Salska and colleagues (2008) studied height preferences among dating partners. In their first study, they reviewed Yahoo! Personals for heterosexual individuals living within 250 miles of Los Angeles, California, and recorded the acceptable range of heights for their dating partners. The following table lists some of the results.

 

Preferences Women Men  
M SD M SD  
Shortest acceptable height, inches 68.9 2.6 60.6 3.7  
Tallest acceptable height, inches 75.3 2.2 69.8 2.7

 

  1. Overall, did men or women show greater variability in their responses? Explain.

______________________________________________________________________

Problem Set 2.3: Range, Variance, and Standard Deviation in Excel

Criterion: Calculate measures of variability in Excel from a group of raw scores.

Data: A sample of likes per post on Facebook: 45, 789, 16, 5, 486, 1, 87, 18, 48, 1

Instructions: Complete the following steps:

  1. Install the data analytics package in Excel.
    • If you are unsure about how to do this, visit Load the Analysis Toolpak in Microsoft Excel, which has tutorials for both Windows and Mac. Used with permission from Microsoft.
  2. Enter the data above into Excel using the variable name Data. In cell A1, type the word “Data.” Then, enter the data above in cells A2 to A11.
  3. In the Toolbar, click Data Analysis, Select Descriptive Statistics, then click
  4. Next to input range type: $A$2:$A$11
  5. Double check that summary statistics has a check next to it.
  6. Click OK. A new sheet will appear to the right with your data.
  7. Copy and paste the descriptive statistics table below.
    • Highlight the range, mean, and standard deviation.

Problem Set 2.5: 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 men and women living on or off campus. The population is summarized in the following table.

  Male Female 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 male participant? _______________________
  2. What is the probability of selecting a female 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 male student, given that he lives off campus? _______________________
  6. What is the probability of selecting a female student, given that she lives on campus? _______________________
  7. What is the probability of selecting a male student, given that he lives on campus? _______________________
  8. What is the probability of selecting a female student, given that she lives off campus? _______________________
  9. What is the probability of selecting a student who lives on campus, given that he is a male? _______________________
  10. What is the probability of selecting a student who lives off campus, given that he is a male? _______________________
  11. What is the probability of selecting a student who lives on campus, given that she is a female? _______________________

Problem Set 2.6: Determining Probability

Criterion: Determine the probability.

Instructions: Read 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 2.7: 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, Baumeister, and DeWall (2007) 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).

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? ___________________________

 

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