Question

Be sure to show your work for problems that require calculation. 1. The table below shows the raw data for the results of a nicotine patch drug trial. The treatment column describes whether the participant received a placebo or the patch, the symptom column describes if the participant described relief from their nicotine cravings or not. Use a critical value of 3.84. (6 points) Treatment Symptoms Placebo No relief Nicotine patch Relief Placebo No Relief Nicotine patch Relief Placebo No relief Nicotine patch Relief Placebo. Relief Placebo relief Nicotine patch Relief Placebo No relief Nicotine patch No relief Nicotine patch No Relief Placebo No relief Treatment Placebo Nicotine patch Nicotine patch Nicotine patch Placebo Nicotine patch Placebo Placebo Placebo Nicotine patch Placebo Nicotine patch Nicotine patch Symptoms No relief No relief Relief Relief Relief Relief No relief No relief No relief Relief Relief Relief Relief a. Create a two-way table for the data. (1 pt) b. Write the null and alternate hypothesis for this test. (.5 pts) c. What are the assumptions of this test? (1 pt) d. Compute the appropriate test statistic. Show all your work including the work for calculating one expected count and all parts of the statistic. (2 pts) e. Write a conclusion for this test (include your check of the assumptions). (1.5 pts) Be sure to show all work

Answer 1

a) Two-way table:

	Relief	No Relief	Total
Placebo	4	9	13
Nicotine patch	10	3	13
Total	14	12	26

b)

Null and Alternative hypothesis:

Ho: Treatment and symptoms are independent.

H1: Treatment and symptoms are dependent.

c) Assumptions:

The data in the cells should be frequencies, or counts of cases rather than percentages or some other transformation of the data.

The levels (or categories) of the variables are mutually exclusive. That is, a particular subject fits into one and only one level of each of the variables.

Each subject may contribute data to one and only one cell in the χ2.

The study groups must be independent.

The value of the cell expected cells should be 5 or more in at least 80% of the cells, and no cell should have an expected of less than one.

d)

Observed Frequencies
	Relief	No Relief	Total
Placebo	4	9	13
Nicotine patch	10	3	13
Total	14	12	26
Expected Frequencies
	Relief	No Relief	Total
Placebo	14 * 13 / 26 = 7	12 * 13 / 26 = 6	13
Nicotine patch	14 * 13 / 26 = 7	12 * 13 / 26 = 6	13
Total	14	12	26
	(fo-fe)²/fe
Placebo	(4 - 7)²/7 = 1.2857	(9 - 6)²/6 = 1.5
Nicotine patch	(10 - 7)²/7 = 1.2857	(3 - 6)²/6 = 1.5

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 5.5714

Critical value:

χ²α = CHISQ.INV.RT(0.05, 1) = 3.84

e) As χ² > χ²α, so we reject the null hypothesis.

There is enough evidence to conclude that treatment and symptoms are dependent.