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

Question

1.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 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.

a.What is the null hypothesis for this test?

b.What is the alternative hypothesis?

c.Fill in the following table.

d.What is the value of X2 for this data?

e.What is the number of degrees of freedom?

f.Use the X2 calculator to compute p (use the right tail option) (LINK BELOW). Provide a screen shot of your calculation. (PLEASE DO NOT ANSWER THIS ENTIRE QUESTION IF YOU CANNOT PROVIDE A SCREEN SHOT)

http://www.statdistributions.com/chisquare/

g.Does this value of p support the null hypothesis at the 5% significance level? (yes or no and explain using your numbers)

(O - E) (O-E)2 (O-E)/E Ball Color Observed Expected0-E) Red 185 115 300 Black um n/a

Explanation / Answer

a) H0: There is no difference between observed and expected frequencies.

b)H1: H0: There is a difference between observed and expected frequencies.

alpha:5%

c)

d) =87.25

e) Degree of freedom=n-1= 2

f) Pvalue=0.0000

g) P<0.05, we reject the H0.

Oi Ei Oi-Ei (O-E)^2 (O-E)^2/E 185 200 -15 225 1.125 115 200 -85 7225 36.125 300 200 100 10000 50 200 sum= 87.25

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