Question

Suppose we are conducting a chi-squared goodness of fit test to test if a data set follows a uniform(0,16) distribution. We gather 30 observations and decide to use 5 equal probability intervals of the form:

[a_0, a₁], [a_1, a₂],[a_2, a₃],[a_3, a₄],[a_4, a₅]

We find our intervals, and find our test statistic to be 9.21.  

If we conduct our test using α = 0.05, would we

a) Reject the null hypothesis

b) Fail to reject the null hypothesis

SHOW WORK

Answer 1

Solution:

For the given distribution, we have

k = 5 intervals

df = k – 1 = 5 – 1 = 4

α = 0.05

Chi-square critical value = 9.49

(by using chi-square table or excel)

We are given

Chi square test statistic = 9.21

Test statistic value is less than critical value, so we fail to reject the null hypothesis.

Answer:

b) Fail to reject the null hypothesis