Question

5. You want to see if smoking marijuana has any effect (positive or negative) on memory span. You pre-test subjects on the memory span measure, then pair up subjects who have the same memory test score. After matching the subjects, you conduct the actual experiment. One member of each of the 15 pairs of subjects is assigned at random to smoke a marijuana cigarette; the other member of each pair is assigned to smoke a cigarette that doesn't contain any of the psychoactive ingredient in marijuana, THC (placebo). After smoking, every subject takes the memory span test again. The results of this second test are tabled below. a. Estimate the mean difference in performance on the memory test at the 95% level of confidence. State in English what your results mean. b. Without actually conducting a hypothesis test, evaluate the hypothesis that there is no effect on memory of smoking marijuana. Explain in 1 sentence the reasoning underlying your conclusion. Pair |123 4 5 6 7 8 9 10 11 12 13 14 15 Marijuana 4 5 6 6 7 7 6 6 3 4 5 5 6 7 7 Placebo 5 6 769 6 5 7 5 5 6 8 7 5 6

Answer 1

(a)

Here we have paired observations so paired t test will be used. Let d = marijuana - placebo

Following table shows the calculations:

Marijuana	Placebo	d=test1-test2	(d-mean)^2
4	5	-1	0.16
5	6	-1	0.16
6	7	-1	0.16
6	6	0	0.36
7	9	-2	1.96
7	6	1	2.56
6	5	1	2.56
6	7	-1	0.16
3	5	-2	1.96
4	5	-1	0.16
5	6	-1	0.16
5	8	-3	5.76
6	7	-1	0.16
7	5	2	6.76
7	6	1	2.56
Total		-9	25.6

Sample size n = 15 Sample sum of difference: Sd =-9 Sample mean of differences: d d=2“ =-9/15 = -0.6 Sample standard deviation of differences: s- (d-d) -=sqrt(25.6/(15-1)) n-1 V =1.3522

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The 95% confidence interval is

Since populaiton SD is unknown so t critical value will be used. Level of significance: a =0.05 Critical value: te=2.145 Degree of freedom: df =n-1=14 The requried confidence interval is: à ft. --0.6 + (1.3522*2.145/sqrt(15)) =-0.6 + 0.7489 =(-1.349,0.149) Excel function for critical value: ETINV(0.05,14) Hence, the required confidence interval is (-1.349,0.149).

(b)

Since confidence interval does not contain zero so we reject the null hypothesis on the basis of confidence interval. There is evidence to conclude that there is no effect on memory of smoking marijuana.