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Before the Start of the Winter Olympics, It Was Expected

question 53

Essay

Before the start of the Winter Olympics, it was expected that the percentages of medals awarded to the top contenders to be as follows.
 Percentages  United States 25% Germany 22% Norway 18% Austria 14% Russia 11% France 10%\begin{array}{lc}&\text { Percentages }\\\text { United States } & 25 \% \\\text { Germany } & 22 \% \\\text { Norway } & 18 \% \\\text { Austria } & 14 \% \\\text { Russia } & 11 \% \\\text { France } & 10 \%\end{array} Midway through the Olympics, of the 120 medals awarded, the following distribution was observed.
 Number of Medals  United States 33 Germany 36 Norway 18 Austria 15 Russia 12 France 6\begin{array}{ll}&\text { Number of Medals }\\\text { United States } & 33 \\\text { Germany } & 36 \\\text { Norway } & 18 \\\text { Austria } & 15 \\\text { Russia } & 12 \\\text { France } & 6\end{array} We want to test to see if there is a significant difference between the expected and actual awards given.
a. Compute the test statistic.
b. Using the p-value approach, test to see if there is a significant difference between the expected and the actual values. Let α = .05.
c. At 95% confidence, test for a significant difference using the critical value approach.

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