Skip to main content
Statistics LibreTexts

14.4: Pineapple on Pizza

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    There is a very passionate and on-going debate on whether or not pineapple should go on pizza. Being the objective, rational data analysts that we are, we will collect empirical data to see if we can settle this debate once and for all. We gather data from a group of adults asking for a simple Yes/No answer.

    Step 1: State the Hypotheses

    We start, as always, with our hypotheses. Our null hypothesis of no difference will state that an equal number of people will say they do or do not like pineapple on pizza, and our alternative will be that one side wins out over the other:

    \[\mathrm{H}_{0}: \text { There is no difference between the number of people who do and do not like pineapple on pizza } \nonumber \]

    \[\mathrm{H}_{A}: \text { There is a difference between the number of people who do and do not like pineapple on pizza} \nonumber \]

    Step 2: Find the Critical Value

    To avoid any potential bias in this crucial analysis, we will leave \(α\) at its typical level. We have two options in our data (Yes or No), which will give us two categories. Based on this, we will have 1 degree of freedom. From our \(\chi^{2}\) table, we find a critical value of 3.84.

    Step 3: Calculate the Test Statistic

    The results of the data collection are presented in Table \(\PageIndex{1}\). We had data from 45 people in all and 2 categories, so our expected values are \(E = 45/2 = 22.50\).

    Table \(\PageIndex{1}\): Results of Data collection
      Yes No Total
    Observed 26 19 45
    Expected 22.50 22.50 45

    We can use these to calculate our \(\chi^{2}\) statistic:

    \[\chi^{2}=\dfrac{(26-22.50)^{2}}{22.50}+\dfrac{(19-22.50)^{2}}{22.50}=0.54+0.54=1.08 \nonumber \]

    Step 4: Make the Decision

    Our observed test statistic had a value of 1.08 and our critical value was 3.84. Our test statistic was smaller than our critical value, so we fail to reject the null hypothesis, and the debate rages on.

    Contributors and Attributions

    • Foster et al. (University of Missouri-St. Louis, Rice University, & University of Houston, Downtown Campus)

    This page titled 14.4: Pineapple on Pizza is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Foster et al. (University of Missouri’s Affordable and Open Access Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.