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)
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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:
χ² = 4.02 (2 decimal places)
Pvalue = 0.2595 (4 decimal places)
Step-by-step 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)