15.3.4: Chapter 5 Lab
- Page ID
- 28618
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Cross‐tabulation and Two Way Tables
Open the Minitab file lab04.mpj from the website.
Here is a description of the data collected from elementary schools in Michigan:
- Gender: (Boy, Girl)
- Grade: 4, 5 or 6
- Age: Age in years
- Ethnicity: White, Other (Yes, that was the way it was reported when this data was collected!)
- Location: Rural, Suburban, Urban
- School: 1=Brentwood Elementary, 2=Brentwood Middle, 3=Ridge, 4=Sand, 5=Eureka, 6=Brown, 7=Main, 8=Portage, 9=Westdale Middle
- Goals: Student's choice in the personal goals: 1=Make Good Grades, 2=Be Popular, 3=Be Good in Sports
- Grades: Rank of "make good grades" (1=most important for popularity, 4=least important)
- Sports: Rank of "being good at sports" (1=most important for popularity, 4=least important)
- Looks: Rank of "being handsome or pretty" (1=most important for popularity, 4=least important)
- 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:
- Cross‐tabulate Gender with Goal and create a two‐way table. Create a clustered bar graph. Paste them both here.
- 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)?
- What is probability that a randomly selected student is a boy? What type of probability is this (Marginal, Joint, or Conditional)?
- What is probability that a randomly selected student is a boy and chooses sports as the most important goal? What type of probability is this (Marginal, Joint, or Conditional)?
- What is the probability ca randomly selected boy chooses sports as the most important goal? What type of probability is this (Marginal, Joint, or Conditional)?
- What conclusions can you make about Gender and Goal?
- Cross‐tabulate Location with Goal and create a two‐way table. Create a pie graphs for Goal with a multiple variable Location on the same graph. Paste the cross‐tabulation and pie graphs here
- What is the probability that a randomly selected student chooses sports as the most important goal?
- What is probability that a randomly selected suburban student chooses sports?
- What is the probability that a randomly selected rural student chooses sports?
- What is the probability that a randomly selected urban student chooses sports?
- What conclusions can you make about Location and Goal?
- Cross‐tabulate any two variables of your choice and create a two‐way table. Create a clustered bar graph. Paste them both here.
- Calculate and explain any marginal probability of your choice.
- Calculate and explain any joint probability of your choice.
- Calculate and explain any conditional probability of your choice.
- What conclusions can you make about these two variables?