Researchers conducted an experiment to measure the effect of a drug on improving

Question

Researchers conducted an experiment to measure the effect of a drug on improving the quality of sleep as determined by how many more minutes of REM sleep were measured for each participant. One group of participants were given the experimental drug; the other (control) group was given a placebo. Does the evidence indicate that the drug improved the amount of REM sleep at a 0.01 level of significance? Answer each of the following parts. Experimental group Control group sample size 35 50 mean sleep improvement 12.8 9.1 sample variance 56.3 61.2 What is the test value for this hypothesis test? Answer: Round your answer to two decimal places. What is the P-value for this hypothesis test? Answer: Round your answer to three decimal places. What is the conclusion of this hypothesis test? Choose one. 1. There is sufficient evidence to show that the experimental drug improved the quality of sleep. 2. There is not sufficient evidence to show that the experimental drug improved the quality of sleep. 3. There is sufficient evidence to show that the quality of sleep is different for the experimental drug than for the control drug. 4. There is not sufficient evidence to show that the control drug decreased the quality of sleep. Answer:

Explanation / Answer

Solution:

From the given information

n1=35 1 = 12.8 s1 = sqrt(56.3) =7.503

n2 = 50 2 = 9.1 s2 = sqrt(61.2) =7.823

H0: 1= 2

H1: 1>2  

test statistic = (1-2) / ((s1^2/n1)+(s2^2/n2))

= (12.8-9.1) / ((7.503^2/35)+(7.823^2/50))
= 2.20

since it is right tailed test

pvalue = 1 - P(Z<=2.20) = 1 - 0.9861
= 0.014

Significance level = 0.01

since p-value > we fail to reject null hypothesis H0

2. There is not sufficient evidence to show that the experimental drug improved the quality of sleep.

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