Given the following contingency table, conduct a test of independence at the 1%

Question

Given the following contingency table, conduct a test of independence at the 1% significance level Use Table 3 Category1 Category2 2 38 28 30 2 Critical value approach a-1. Choose the null and alternative hvpotheses O Ho. The two categories are dependent: HA: The two categories are independent. O Ho: The two categories are independent.; HA: The two categories are dependent. a-2. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) df a-3. Specify the decision rule. (Round your answer to 3 decimal places.) Reject Ho if > a-4. What is your conclusion? O Do not reject Ho, the two categories are not dependent O Do not reject Ho, the two categories are dependent O Reject Ho, the two categories are dependent 0 Reject Ho, the two categories are not dependent p-value approach b-1. Approximate the p-value O 0.050

Explanation / Answer

a1) option B) is correct

a2)

test statistic = 2.1247

a3)

reject if TS > 3.84

a4)

since TS < critical value

option A) is correct

b1) p-value = 0.145

option E) is correct

b2)

option C) is correct

c1 c2 total r1 28 38 66 r2 30 66 96 total 58 104 162 Oi 28 38 30 66 Ei 23.62963 42.37037 34.37037 61.62963 TS (O--Ei)^2/Ei 0.808313 0.45079 0.555715 0.309918 2.124736 critical value 3.84 p-value 0.144937728

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