Question

a) The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the χ2-test statistic, and use the χ2-distribution to find the p-value of the test.

Category	A	B	C	D
Observed    (Expected)	80(70)	130(140)	195(210)	295(280)

Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places.
chi-square statistic = ____________________
p-value = ____________________

b) A null hypothesis for a goodness-of-fit test and a frequency table from a sample are given.

H0: pa=pb=pc=pd=0.25
Ha: Some pi≠0.25

A	B	C	D	Total
208	225	198	209	840

Find the expected count for the category labeled B.

The expected count is __________________________

Find the contribution to the sum of the chi-square statistic for the category labeled B.
Round your answer to three decimal places.
The contribution for the category labeled B is ____________________

Find the degrees of freedom for the chi-square distribution for this table.
_________________ degree(s) of freedom

Answer 1

a)

chi-square statistic :

O : Observed counts

E : Expected counts

Degrees of freedom = number of categories - 1 = 4-1=3

for 3 degrees of freedom;

p-value = 0.2595

chi-square statistic = 4.11

p-value = 0.2595

b)

Expected count for category B : Eb = p_b * Total = 0.25 * 840 = 210

The expected count is 210

Contribution to the sum of the chi-square statistic for the category labeled B. =

O_b : Observed Count for the category B = 225

Contribution to the sum of the chi-square statistic for the category labeled B. =

The contribution for the category labeled B is 1.071

Degrees of freedom for the chi-square distribution for this table = number of categories - 1 = 4-1 =3

3 degree(s) of freedom