3. The table below summarizes results from an experiment involving randomly sele

Question

3. The table below summarizes results from an experiment involving randomly selected subjects who experience some degree of sleeplessness. Some of the subjects were treated with a drug. while others were given a placebo. Experienced Improvement Did Not Experience Any Improvement 49,875 Treatment Group Placebo Group 10,222 10.587 53,252 Use the methods of Chapter 11 (Chi Square) to test for independence between the treatment and placebo What do yoù conclude? Does it appear that the treatment is effective? What does the result suggest about the decision to distribute the treatment? group and whether the subject experienced improvement in the degree of sleeplessness.

Explanation / Answer

Here we will use chi-square test for independence between the treatment and placebo group and whether there is affect of experiment on degree of sleeplessness.

Here observed table

Here expected values will be calculated as such

(a) for Treatment and experienced improvement = (20809 * 60097)/ 123936 = 10090.26

for Treatment and not expereience improvement = (103127 * 60097)/123936 = 50006.64

similarly we will calculate it for placebo group too aur we can just minus it from the total value.

Expected Table

So Chi - square value

X2 = (O -E)2/E

We will find the partie chi - square for each cell and then sum it

so for treatment - experienced = (10222 - 10090.36)2 /10090.36 = 1.72

Chi - square table

So Xcr 2 for dF = 1 and alpha = 0.05

Critical chi - square = 3.8415

p- value == Pr(X2 > 4.007,1) = 0.0453

so it is significant at alpha = 0.05 but not at 0.01 level.

So, yest the treatment is effective. so the result suggest that the Treament group is affective for sleepness treatment cure.

Experienced Improvement No improvement Total Treatment 10222 49875 60097 Placebo 10587 53252 63839 Total 20809 103127 123936

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