# Statistics

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1. The Chi-square distribution, used in the Chi-square test of independence, varies in shape by degrees of freedom. What does the Chi-square distribution look like for 4 degrees of freedom.
A) Unimodal and symmetric.
B) Bimodal and symmetric.
C) Unimodal and skewed to the left.
D) Unimodal and skewed to the right.

2.The Chi-square distribution, used in the Chi-square test of independence, varies in shape by degrees of freedom. What does it mean when the Chi-square value is small and the p-value is large?
A) As the Chi-square value gets small, the probability value gets large. In this case you fail to reject Ho and believe the events are independent.
B) As the Chi-square value gets small, the probability value gets large. In this case you fail to reject Ho and believe the events are not independent.
C) As the Chi-square value gets small, the probability value gets large. In this case you reject Ho and believe the events are not independent.
D) As the Chi-square value gets small, the probability value gets large. In this case you reject Ho and believe the events are independent.

3. The χ2-test for independence is a useful tool for establishing a causal relationship between two factors.

A) True
B) False

1. B
2. D
3. A

• Statistics -

1. D
Chi Square distributions are positively skewed (skewed to the right). As the degrees of freedom increases, the Chi Square distribution will approach a normal symmetrical distribution. Smaller degrees of freedom will skew more to the right.

2. A
Ho: The variables are independent.
Ha: The variables are not independent.
(Large p-values result in failing to reject Ho.)

3. B
The alternative hypothesis (Ha) suggests that the variables are related, but the relationship is not necessarily a causal one.

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