A spinner is divided into six areas of equal size, each with a different color (

Question

A spinner is divided into six areas of equal size, each with a different color (blue, yellow, red, green, white and orange). When the spinner is spun, each color should be selected by the spinner approximately 1/6 of the time. A student suspects that a certain spinner is defective. The suspected spinner is spun 90 times. The results are shown below. Perform a goodness-of-fit test to test the student's claim at a level of significance of 0.05. State the conclusion of the test using precise statistical language.

Explanation / Answer

for above degree of freedom =n-1=5 ; chi stat =3.0667

for this p value =0.6897

as p value is hiogher then 0.05 level we can not conclude that spinner is defective.

observed Expected Chi square Color Probability O E=total*p =(O-E)^2/E blue 1/6 17.000 15.00 0.27 yellow 1/6 15.000 15.00 0.00 red 1/6 16.000 15.00 0.07 green 1/6 19.000 15.00 1.07 white 1/6 11.000 15.00 1.07 orange 1/6 12.000 15.00 0.60 1 90 90 3.0667

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