Testing for Equally Likely Categories Here are the observed frequencies from thr

Question

Testing for Equally Likely Categories Here are the observed frequencies from three categories: 5, 5, 20. Assume that we want to use a 0.05 significance level to test the claim that the three categories are all equally likely

a. What is the null hypothesis?

  H0 : 1       2             3

b. What is the expected frequency for each of the three categories?

c. What is the value of the test statistic?

X2 =

d. What is the critical value?

X2 =

e. What do you conclude about the given claim?

There __________    sufficient evidence to warrant the rejection of the claim

Explanation / Answer

a)   H0 : 1 = 2 = 3

b) The expected frequency for each of the three categories are (5+5+20)/3 = 10, 10, 10

c)

Chisquare value = 15

d) Critical X^2: 5.991471

e) Here Chisquare value > Chsiquare critical value, so we reject H0

Thus, there is sufficient evidece to warrant the reject of the claim

Observed Expected freq Oi freq Ei (Oi-Ei)^2/Ei 5 10 2.5 5 10 2.5 20 10 10 Total = 15

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