The document presents a hypothesis test comparing observed category frequencies to expected frequencies under the null hypothesis. The null hypothesis states that 40% of observations fall in category A, 40% in B, and 20% in C. A sample of 60 was taken with 30 in A, 20 in B, and 10 in C. The chi-square test statistic is calculated to be 2.503, which is less than the critical value of 9.21 at the 0.01 significance level. Therefore, the null hypothesis is not rejected.

1. the following hypothesis are given
H0: forty percent of the observations are in category A, 40 percent are in B, and 20 percent are
in C
H1: The distribution of the observations is not as described in H0
category
a 30
b 20
c 10
We took a sample of 60 with the results to the left.
A. state the decision rule using the .01 significance level
B. compute the value of chi-square
C. What is your decision regarding H0?
Solution
Expected are .40*60= 24 A .40*60= 24 B .20 *60 12 C Test statistic is the sum of
(Observed -Expected)^2/ Expected (30-24)^2/24 + (20-24)^2/24 + (10-12)^2/12 1.5 + 0.67 +
0.3333= 2.503 Degrees of freedom are 3-1=2 Checking chi square critical value at .01 level is
9.21. Decision rule is reject null hypothesis if test statistic is > 9.21 Do not reject null hypothesis
as 2.50<9.21.