In a televised game show, contestants are asked to pick what is behind Door #1,

Question

In a televised game show, contestants are asked to pick what is behind Door #1, Door #2, Door #3, and Door #4. The only difference the contestant can see is the number on the door. If contestants do not have a preference for particular numbers, then each door should have a 25% chance of being selected. The game producers, however, have decided to analyze the contestant’s choices to see if they have a preference for certain doors, so they gathered the following data on door choices: out of 160 trials, contestants made the following choices: Door #1 was selected 38 times; Door #2 was selected 42 times; Door #3 was selected 42 times; Door number 4 was selected 38 times. What is the Chi Square statistic in this example?

Explanation / Answer

here as each door is expected to be opened 25% of times

applying chi square test:

  Chi Square test statistic =0.40

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E Door 1 0.250 38.000 40.00 0.10 Door 2 0.250 42.000 40.00 0.10 Door 3 0.250 42.000 40.00 0.10 Door 4 0.250 38.000 40.00 0.10 1 160 160 0.40

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