A new drug used as an aid for those who ant to quit smoking is tested. The adverse reaction of nausea has been studied in clinical trials, and the table summarizes results. Find the test statistic needed to test the claim that nausea is independent of whether the subject took a placebo or the new drug. Nausea 10,145
No nausea 795, 122
To test the claim that nausea is independent of whether the subject took a placebo or the new drug, we can use the chi-squared test for independence.
First, we need to calculate the expected values for each cell in the contingency table.
Total = 10,145 + 795 + 122 = 11,062
Total with Nausea = 10,145
Total without Nausea = 795 + 122 = 917
Expected value for Nausea and Placebo = (10,145/11,062) * 917 = 843
Expected value for Nausea and New Drug = (10,145/11,062) * 917 = 74
Expected value for No Nausea and Placebo = (917/11,062) * 917 = 76
Expected value for No Nausea and New Drug = (917/11,062) * 917 = 76
Now we can calculate the test statistic:
chi-squared = Σ((Observed - Expected)^2 / Expected)
= ((10,145 - 843)^2 / 843) + ((795 - 74)^2 / 74) + ((122 - 76)^2 / 76) + ((917 - 76)^2 / 76)
= (9302.38 + 8719.51 + 142.95 + 10122.11)
= 28286.95
The degrees of freedom for the chi-squared test for independence is (rows - 1) * (columns - 1) = 1 * 1 = 1
Using a chi-squared distribution table or a statistical software, we can find the critical value for a significance level, say α = 0.05. If the calculated chi-squared value is greater than the critical value, we reject the null hypothesis and conclude that nausea is not independent of whether the subject took a placebo or the new drug.