PART A: US Presidential Election
A student in the USA is researching the association (if any) between the public interest in the presidential race and country of birth. He asks 993 Americans to rate their interest level and to state the country in which they were born. Use a chi-squared test to determine if there is evidence that public interest in the presidential race and country of birth are related.
|
|
USA
|
China
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Australia
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Total
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Very Interested
|
276
|
41
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17
|
334
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|
Mildly Interested
|
196
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174
|
47
|
417
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|
Don't Care
|
130
|
97
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15
|
242
|
|
Total
|
602
|
312
|
79
|
993
|
(Q1) Enter this data into SPSS, with one column containing Interest (very/mild/don't care), one column containing country of birth (USA/China/Australia) and one column containing the frequency in each group. Use Data>Weight Cases to assign weights based on the number of characters described in each row (i.e. select the last column 'Frequency' for weights).
a) Construct a two-way table of Interest x Country in SPSS. Include row and column percentages. To provide an answer to this question, copy and paste the two-way table.
b) What percentage of people born in the USA are very interested in the presidential election?
c) What percentage people who don't care about the presidential election were born in Australia?
d) Use the appropriate statistical test and a 5% level of significance to determine whether there is an association between interest in the presidential election and country of birth. State the null and alternative hypotheses, corresponding p-value with your decision and conclusion.
PART B: Student Grades
(Q2) A high school student is accused of cheating so the principal must investigate whether or not the accusation is true. If she finds the student guilty of cheating she will expel the student. If she finds no evidence of cheating the student will be allowed to graduate with their current grade.
a) State your null and alternative hypothesis
b) Describe a Type I error in this context.
c) Describe a Type II error in this context.
PART C: Video Games
This data set was adapted from Peck, R., Olsen, C. and Devore, J. (2012) Introduction to Statistics & Data Analysis. Original source: "Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth" (Pediatrics [2009]: 870-876).
The SPSS worksheet called video.sav contains a subset of results of an experiment carried out to assess the attractiveness of video games for young game players. Participants read the same description of a new video game, which was accompanied by one of three age recommendations. The data contains the age recommendation and the participants' rating of how much they wanted to play the game on a scale of 1 to 10. For the following questions use a 5% level of significance when required.
(Q3) Construct multiple box plots with a box for each age recommendation and find summary statistics (measures of central tendency and variation). What do the box plots and summary statistics tell you about the differences or similarities in the ratings for each of the age recommendations?
(Q4) Check whether all the assumptions for an Analysis of Variance (ANOVA) are met.
(Q5) Perform an ANOVA to determine whether there are any significant differences between the ratings of the three different age recommendations. State your null and alternative hypotheses, the p-value of the test, your decision, and conclusion in context.
(Q6) If you find a significant difference in question 5, perform appropriate multiple comparison procedures to determine where the differences lie. Again, in one or two sentences, summarise your findings in context (so that anyone can understand you).
PART D: Questionnaire Analysis
The questions from the following survey were taken from "Teaching Statistics: A Bag of Tricks"
Computer Games Survey
1. Which of the following best describes your current situation?
Full-time student with no regular paid work
Full-time student with some regular paid work
Part-time student with full-time job
Part-time student-other
2. How much time did you spend last week playing video and/or computer games?
3. What types of games do you play? (Tick all that apply)
Action (e.g. Doom, Street Fighter)
Adventure (e.g. King's Quest, Myst, Return to Zork, Ultima)
Simulation (e.g. Flight Simulator, Rebel Assault)
Sports (e.g. FIFA Soccer, WiiSports)
Strategy/Puzzle (Civilization, SimCity)
4. You Are: Male Female
This part of the assignment is to give you practical experience in setting up the data set for a questionnaire in SPSS and planning on the type of analysis you could perform.
(Q7) Complete 10 of the questionnaires given above and enter the data into SPSS (you can ask 10 people or make up the data -this is a pilot test for the method). Set up an SPSS data file, defining and labelling the necessary variables to record the survey data. Use File>Display Data File>Working File to provide a record of your variable definition. To provide an answer to this question, copy and paste the file information.
(Q8) Using your dataset, summarise the responses to each of the questionnaire questions separately. Include descriptive statistics and visual displays.
(Q9) Which statistical test would you use to answer the following questions? (You do not need to conduct the test, just state which one is appropriate, e.g. an answer might be "chi-square test").
a) Does the average time spent playing video games vary with student's current situation (Q1)?
b) Do female students spend on average less time playing video games than male students?
c) Do students spend at least 10 hours, on average each week playing videogames?
d) Is there a relationship between student's current situation (Q1) and gender?