Question

In: Statistics and Probability

The null hypothesis and the alternate hypothesis are: H0: The frequencies are equal. H1: The frequencies...

The null hypothesis and the alternate hypothesis are:

H0: The frequencies are equal.
H1: The frequencies are not equal.

Category f0
A 10
B 30
C 30
D 10
  1. State the decision rule, using the 0.05 significance level. (Round your answer to 3 decimal places.)

  1. Compute the value of chi-square. (Round your answer to 2 decimal place.)

  1. What is your decision regarding H0?

Solutions

Expert Solution

The degrees of freedom = n - 1 = 4 - 1 = 3

The Critical value at = 0.05 is 7.815

(a) Therefore the decision rule is Reject H0, if > 7.815

____________________________________

(n) Each expected value = (10 + 30 + 30 + 10) / 4 = 80 / 4 = 20

Observed Expected O-E (O-E)2 (O-E)2/E
1 10 20 -10 100 5.000
2 30 20 10 100 5.000
3 30 20 10 100 5.000
4 10 20 -10 100 5.000
Total 80 80 20.00

test = 20.00

_______________________________________________

(c) Since testis > 7.815, Reject H0.

_____________________________________________

The Conclusion: There is sufficient evidence at the 95% level of significance to conclude that the frequencies are not equal.

______________________________________________


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