Math 10 MPS - Lab 3 – Cross-tabulation and Two Way Tables & Discrete Random Variables Open the Minitab file popular.mpj from the website Here is a description of the data collected from elementary schools in Michigan: 1. Gender: (Boy, Girl) 2. Grade: 4, 5 or 6 3. Age: Age in years 4. Ethnicity: White, Other (Yes, that was the way it was reported when this data was collected!) 5. Location: Rural, Suburban, Urban 6. School: 1=Brentwood Elementary, 2=Brentwood Middle, 3=Ridge, 4=Sand, 5=Eureka 6=Brown, 7=Main, 8=Portage, 9=Westdale Middle 7. Goals: Student's choice in the personal goals: 1=Make Good Grades, 2=Be Popular, 3=Be Good in Sports 8. Grades: Rank of "make good grades" (1=most important for popularity, 4=least important) 9. Sports: Rank of "being good at sports" (1=most important for popularity, 4=least important) 10. Looks: Rank of "being handsome or pretty" (1=most important for popularity, 4=least important) 11. Money: Rank of "having lots of money" (1=most important for popularity, 4=least important) Cross Tabulation is a method of taking pairs of categorical variables and creating a two-way table. The command can be found on the menu bar STAT>TABLES>CROSSTABULATION. Choose two data items and check that you want count, row percents and column percents. You can also make a clustered bar graph GRAPHS>BAR GRAPH>CLUSTERED. The example shows gender cross-tabulated with grade level: There are three questions with parts on the next three pages. Be sure to answer them all. 1. Cross-tabulate Gender with Goal and create a two-way table. Create a clustered bar graph. Paste them both here. a. What is the probability a randomly selected student chooses sports as the most important goal? What type of probability is this (Marginal, Joint, or Conditional)? b. What is probability that a randomly selected student is a boy? What type of probability is this (Marginal, Joint, or Conditional)? c. What is probability that a randomly selected student is a boy and chooses sports as the the most important goal? What type of probability is this (Marginal, Joint, or Conditional)? d. What is the probability a randomly selected boy chooses sports as the most important goal? What type of probability is this (Marginal, Joint, or Conditional)? e. What conclusions can you make about Gender and Goal? 2. Cross-tabulate Location with Goal and create a twoway table. Create a pie graphs for Goal with a multiple variable Location on the same graph. Paste the cross-tabulation and pie graphs here a. What is the probability a randomly selected student chooses sports as the most important goal? b. What is probability that a randomly selected suburban student chooses sports? c. What is the probability a randomly selected rural student chooses sports? d. What is the probability a randomly selected urban student chooses sports? e. What conclusions can you make about Location and Goal? 3. Cross-tabulate any two variables of your choice and create a two-way table. Create a clustered bar graph. Paste them both here. a. Calculate and explain any marginal probability of your choice. b. Calculate and explain any joint probability of your choice. c. Calculate and explain any conditional probability of your choice. d. What conclusions can you make about these two variables? For the next question, open minitab file RandomVariables.MPJ project. 4. Find Probabilities for a Binomial Random Variable (MINITAB>CALC>PROBABILITY DISTRIBUTIONS) (put the needed values of x under the column x for Binomial) In a poll conducted January 2015, 72% of American adults put protecting freedom of speech ahead of not offending others. Assume this is the true proportion. You sample 64 American adults. Let X be the number in the sample who put protecting freedom of speech ahead of not offending others. a. Determine the probability that 44 American adults or less in the sample put protecting freedom of speech ahead of not offending others. (Cumulative Probability) Is this result unusual? b. Determine the probability that 56 American adults or more in the sample put protecting freedom of speech ahead of not offending others. (Cumulative Probability plus Rule of Complement) Is this result unusual? c. Create a Probability Distribution Plot of this binomial distribution (Under Graph Menu in Minitab). d. What is the mean, variance and standard deviation of X? e. Use the empirical rule to determine between what two values would you expect to find 95% of value of the random variable X? Is the result consistent with the graph?