The new medical drug used SNA for those who want to stop smoking is tested. The adverse reaction of nausea has been studying and clinical trials in the table summarizes results. Find the test statistic needed to test the claim that nausea is independent of whether the subject took up placebo or the new drug. Nausea placebo new medical drug 10, 145 no nausea placebo new medical, drug 795, 122

Question

The new medical drug used SNA for those who want to stop smoking is tested. The adverse reaction of nausea has been studying and clinical trials in the table summarizes results. Find the test statistic needed to test the claim that nausea is independent of whether the subject took up placebo or the new drug. Nausea placebo new medical drug 10, 145 no nausea placebo new medical, drug 795, 122

Answer 1

To test the claim that nausea is independent of whether the subject took the placebo or the new drug, we need to calculate the test statistic for independence, which is the Chi-square statistic.

First, we need to set up a contingency table with the given data:

Nausea No Nausea
Placebo 10 145
New Drug 795 122

Next, we need to calculate the expected values for each cell in the contingency table under the assumption that nausea is independent of whether the subject took the placebo or the new drug. To do this, we calculate the row and column totals, and then use these totals to calculate the expected values:

Row totals:
Placebo: 10 + 145 = 155
New Drug: 795 + 122 = 917

Column totals:
Nausea: 10 + 795 = 805
No Nausea: 145 + 122 = 267

Expected values:
For cell (1,1):
Expected = (Row Total for Placebo) * (Column Total for Nausea) / (Total number of observations)
= 155 * 805 / 1082
= 115.38

For cell (1,2):
Expected = (Row Total for Placebo) * (Column Total for No Nausea) / (Total number of observations)
= 155 * 267 / 1082
= 38.62

Similarly, you can calculate the expected values for cells (2,1) and (2,2).

Once you have the expected values, you can calculate the Chi-square statistic using the formula:

Chi-square = ∑[(Observed - Expected)^2 / Expected]

Finally, compare the calculated Chi-square statistic to the critical value from the Chi-square distribution with (number of rows - 1) * (number of columns - 1) degrees of freedom to determine if there is a significant relationship between nausea and the type of drug taken. If the calculated Chi-square statistic is greater than the critical value, then we reject the null hypothesis of independence.