Question

Does the data meet the conditions for the chi-square test?

StatCrunch Instructions: Test of Independence Using Technology

No risk. for alcohol problems Moderate to Severe risk for alcohol problems 793 309 1102 Participated in 911 rescue 441 110 551 Did Not Participate in 911 rescue 419 1653 1234

Next we will use StatCrunch to calculate the expected counts:

• Enter Yes and No in column var1.
• Enter the observed counts as they appear in the table above (not including the totals) into columns var2 and var3.
• Rename: var1 as "911", var2 as "No Risk" and var3 as "M to S Risk"
• Choose Stat -> Tables -> Contingency -> with summary
• Select the columns: "No Risk" and "M to S Risk"
• Select Row labels in: "911"
• Press Next
• Check "Expected Count" and "Chi-Square"

part 2

In the previous activity, we carried out the chi-square test using StatCrunch and obtained the following output:

Contigency table results:

Rows: 911

Columns: None

State your conclusion in context. Also explain what the P-value means as a conditional probability based on the null hypothesis.

Answer 1

The level of significance is not given in the problem, so I am assuming it to be α = 0.05

Now p- value = 0.0004

Since 0.0004 < 0.05, we reject the null hypothesis and accept the alternative hypothesis

Conclusion: The two variables in question are dependent

p- value = 0.0004 is the probability of rejecting the null hypothesis while it is actually true.