This problem is the check to see whether you understand the X-squared test. Ther

Question

This problem is the check to see whether you understand the X-squared test. There are only 2 test columns, so you cannot use the X-squared Goodness of Fit applet from the previous problem 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 3: 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 200 times. You obtain 165 red balls and 35 black balls. Using a X- squared test, determine whether or not your results supports the 3: 1 claim. a. What is the null hypothesis for this test? b. What is the alternative hypothesis? c. Fill in the following table.

Explanation / Answer

Since red and black balls are in ratio 3:1 so in 200 times expected ferqeuncy for red balls is

E(red ) = (200*3) / (3+1) = 150

and expected frequency of black balls is

E(black) = (200*1) / (3+1) = 50

(a)

The null hypothesis is

H0: Ratio of red and black balls is 3:1.

(b)

The alternative hypothesis is

Ha: Ratio of red and black balls is not 3:1.

(c)

Following table shows the calculations for chi square test statistics:

Ball Color Observed, O Expected, E (O-E) (O-E)^2 (O-E)^2/E Red 165 150 15 225 1.5 Black 35 50 -15 225 4.5 Sum 200 200 0 6

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