The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis

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 = ____________________

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Thiên Di 3 years 2021-07-31T00:42:45+00:00 1 Answers 11 views 0

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  1. Doris
    0
    2021-07-31T00:43:57+00:00
    Reply

    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)

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