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Before the Start of the Winter Olympics, It Was Expected

Question 70

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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.

Correct Answer:

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a. χ2 = 7.69
b. p-value is lar...

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