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.
$\begin{array}{lc}&\text { Percentages }\\\text { United States } & 25 \% \\\text { Germany } & 22 \% \\\text { Norway } & 18 \% \\\text { Austria } & 14 \% \\\text { Russia } & 11 \% \\\text { France } & 10 \%\end{array}$ Midway through the Olympics, of the 120 medals awarded, the following distribution was observed.
$\begin{array}{ll}&\text { Number of Medals }\\\text { United States } & 33 \\\text { Germany } & 36 \\\text { Norway } & 18 \\\text { Austria } & 15 \\\text { Russia } & 12 \\\text { France } & 6\end{array}$ 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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Definitions:

Behavior Modification

A technique or therapy aimed at changing undesirable behaviors through rewards, punishments, or other reinforcement strategies.

Reinforcing Desired Behaviors

A technique in behavior therapy and conditioning involving rewards or positive feedback to encourage the repetition of specific actions or conduct.

Systematically Desensitizing

A therapeutic technique used to reduce fear or anxiety towards a particular object or situation by gradually exposing the subject to the object or situation in a controlled manner.

Test Anxiety

A psychological condition in which individuals experience extreme distress and anxiety in testing situations, potentially impairing their performance.