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PSYC FPX 4700 Assessment 2 Central Tendency and Probability

Name

Capella University

PSYC FPX 4700 Statistics for the Behavioral Sciences

Prof. Name

Date

Central Tendency and Probability

Problem Set 2.1: Properties of the Mean

 To investigate perception, a researcher chose a group of 12 individuals. Each participant was asked to hold a pair of objects, one in each hand, that varied in weight but were identical in size. They were instructed to indicate when they first detected a difference in the weight of the two objects. The table below presents the weight differences (in pounds) at the point when participants initially perceived a difference.

Difference in Weight (pounds)

4

8

9

5

12

7

6

15

10

4

8

8

Determine the following values for this dataset:

Mean:
Median:
Mode(s): ___

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

Gilman and colleagues (2008) assessed overall life satisfaction in a sample of 1,338 adolescents from two individualistic countries (Ireland, United States) and two collectivist countries (China, South Korea) using the Multidimensional Students’ Life Satisfaction Scale (MSLSS). The table below displays the average MSLSS scores for the participants.

Nation
Gender
Mean Score (Men)
Mean Score (Women)

United States

Men

4.39

 

United States

Women

 

4.61

Ireland

Men

4.37

 

Ireland

Women

 

4.64

China

Men

4.41

 

China

Women

 

4.56

South Korea

Men

3.92

 

South Korea

Women

 

3.78

Among which demographic was overall life satisfaction the lowest on average? Among which demographic was overall life satisfaction the highest on average? 

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

Salska and colleagues (2008) investigated height preferences among dating partners. In their initial study, they analyzed Yahoo! Personals for heterosexual individuals residing within 250 miles of Los Angeles, California, and documented the acceptable height range for their dating partners. The table below presents some of their findings.

Preferences
Women (inches)
Men (inches)

Minimum permissible height

68.9

60.6

Maximum permissible height

75.3

69.8

Did men or women show greater variability in their responses? Explain.

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

A dataset representing the number of likes per post on Facebook includes these values: 45, 789, 16, 5, 486, 1, 87, 18, 48, 1.

Problem Set 2.4: Range, Variance, and Standard Deviation in JASP

 Utilize the dataset likes.jasp, which contains a sample of likes per post on Facebook: Is the mean you calculated the same as the mean found in Problem Set 2.3? ___

Problem Set 2.5: Probability and Conditional Probability 

Researchers frequently explore the probability of specific sampling outcomes. For example, they might inquire about the probability that an individual with certain characteristics will be chosen for a study. This task involves selecting one participant from a hypothetical student population, including both new and returning students living on or off-campus. The population details are summarized in the table provided.

Problem Set 2.6: Determining Probability

 A 2009 brief report by the National Center for Health Statistics (NCHS) from the Centers for Disease Control and Prevention (CDC) indicates that approximately 6% of women in the United States marry for the first time by age 18, 50% by age 25, and 74% by age 30. Using this information, calculate the probability that in a family with two daughters, both daughters will be married by each of the following ages:

PSYC FPX 4700 Assessment 2 Central Tendency and Probability

18 years of age:
25 years of age:
30 years of age: ___

Problem Set 2.7: Understanding Normal Distribution

Stillman et al. (2007) carried out a study where participants listened to a variety of jokes. To gauge their humor, 86 undergraduate students were asked to rate each joke on a scale from 1 (very unfunny) to 21 (very funny). A “lawyer joke” was rated as one of the most amusing, receiving an average rating of 14.48 with a standard deviation of 4.38 (M ± SD).

Assuming the data follows a normal distribution:

  • What rating corresponds to the top 10% of participant ratings for this joke?
  • How many of the 86 undergraduates rated the joke at least 10?
Problem Set 2.8: Calculating z Scores in JASP

Using the dataset ratings.jasp, which records how senior citizens rated the Internet on a scale of 1 to 10 (with 1 being “really distrust it” and 10 being “completely trust it”):

Which number of ratings is closest to the z score of 0?

References

Centers for Disease Control and Prevention. (2009). National Center for Health Statistics Brief Report. [Data file]. Retrieved from [URL]

Gilman, R., & et al. (2008). Multidimensional Students’ Life Satisfaction Scale. [Data file]. Retrieved from [URL]

Salska, I., & et al. (2008). Height preferences among dating partners. [Data file]. Retrieved from [URL]

PSYC FPX 4700 Assessment 2 Central Tendency and Probability

Stillman, T., & et al. (2007). Judging the humorousness of “lawyer” jokes. [Data file]. Retrieved from [URL]



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