10. (10 points) This problem is the check to see whether you understand the X-sq

Question

10. (10 points) This problem is the check to see whether you understand the X-squared t There are only 2 test columns, so you cannot use the from the previous problem X-squared Goodness of Fit applet as it requires 3 or more test intervals. You are told that a bag contains red and black balls which are in a ratio of 2:1. You test this claim by drawing one ball out of the bag and noting its color. Then you replace the drawn ball back into the bag. Thoroughly shake the bag, and draw another ball. You repeat this process 300 times. You obtain 185 red balls and 115 black balls. Using a X- squared test, determine whether or not your results supports the 2:1 claim. What is the null hypothesis for this test? b. a. What is the alternative hypothesis? c. Fill in the following table. Ball Color Observed Expected (O-E) (O-ByO-EyE Red Black Sum 185 115 300 n/a

Explanation / Answer

a) null hypothesis: Ho: our result follows 2:1 distribution.

b)alternate hypothesis: Ha: our result does not follow 2:1 distribution

c)

proportion(p) ball color Observed Expected (O-E) (O-E)2 (O-E)2/E 2/3 red 185 200 -15 225 1.125 1/3 black 115 100 15 225 2.25 sum 300 300 3.375

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