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
Are my answers correct?
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.
1. The Chi-square distribution is a probability distribution that is used in statistical tests, such as the Chi-square test of independence. The shape of the Chi-square distribution depends on the degrees of freedom. In this case, since the question is asking about 4 degrees of freedom, the Chi-square distribution would be unimodal and symmetric. Therefore, the correct answer is A) Unimodal and symmetric.
2. In the context of hypothesis testing using the Chi-square test of independence, the Chi-square value is a measure of the difference between the observed and expected frequencies. The p-value, on the other hand, represents the probability of obtaining a Chi-square value as extreme as the one observed, assuming the null hypothesis is true.
When the Chi-square value is small and the p-value is large, it means that the observed difference between the frequencies is not statistically significant. In other words, there is not enough evidence to reject the null hypothesis, which states that the variables being tested are independent.
Therefore, the correct answer is 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.
3. The statement that the χ2-test for independence is a useful tool for establishing a causal relationship between two factors is false. The Chi-square test of independence examines the relationship between two categorical variables, but it does not imply causation. It only determines whether there is an association or dependence between the variables.
Therefore, the correct answer is B) False.
Based on the explanations given, the correct answers are:
1. A) Unimodal and symmetric.
2. 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.
3. B) False.