Question

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 = ____________________

Answer 1

χ² = 4.02 (2 decimal places)

Pvalue = 0.2595 (4 decimal places)

Explanation:

Given the data:

Category A B C D

Observed (Expected) 80(70) 130(140) 195(210) 295(280)

The Chisquare statistic (χ²) is given by :

χ² = Σ(observed - Expected)² / Expected

χ² = (80-70)²/70 + (130-140)²/140 + (195-210)²/210 + (295-280)²/280

χ² = 1.4285714 + 0.7142857 + 1.0714285 + 0.8035714

χ² = 4.017857

χ² = 4.02 (2 decimal places)

Using the Chisquare Pvalue calculator :

df = n - 1 = 4 - 1 = 3

Pvalue = 0.259548

Pvalue = 0.2595 (4 decimal places)