Question

Researchers have looked for a possible relationship between marijuana smoking and a deficit in performance on a task that measures short-term memory. The memory test utilized in the research was the digit-span task from the Wechsler Adult Intelligence Scale (WAIS). Two groups of ten subjects were tested on the memory task. One group claimed to have never smoked marijuana and the other group claimed to smoke marijuana regularly. The following data is the participant’s scores on the memory task:

Non-Smokers                   Smokers
18                       16
22                       20
21                       14
17                       21
20                       20
17                       18
23                       13
20                       15
22                       17
21                       21

Answer 1

Let us assume that the observations are independent and are drawn from a Normal population. Let us denote by subscript 1 as Non smokers and 2 by smokers. Since it is claimed that marijuana smoking result in deficit performance in short term memory, we shall use a one sided hypothesis.

The null hypothesis:

(Marijuana smoking reduces short term memory)

Level of significance :

First let us calculate the mean and Sd of the data by constructing a table of squares:

	Non smokers	Smokers	x1^2	x2^2
	18	16	324	256
	22	20	484	400
	21	14	441	196
	17	21	289	441
	20	20	400	400
	17	18	289	324
	23	13	529	169
	20	15	400	225
	22	17	484	289
	21	21	441	441
Total	201	175	4081	3141

The test statistic: We shall be applying a two sample independent t-test for the data.

will follow a t-distribution with 10+10-2=18 df.

where is the pooled variance of the data.

  

The critical region of the test is

Since, the calculated value of t falls in the region of rejection, we reject the null hypothesis.The p-value is p=0.0183.

Hence, we conclude that there is enough evidence to claim that Marijuana smoking results in deficit of short term memory loss.

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t-Test: Two-Sample Assuming Equal Variances
	Non smokers	Smokers
Mean	20.1	17.5
Variance	4.544444444	8.722222
Observations	10	10
Pooled Variance	6.633333333
Hypothesized Mean Difference	0
df	18
t Stat	2.257316413
P(T<=t) one-tail	0.018326128
t Critical one-tail	1.734063607
P(T<=t) two-tail	0.036652256
t Critical two-tail	2.10092204