It is known that caffeine has a lot of cognitive benefits. A researcher decides
ID: 3182199 • Letter: I
Question
It is known that caffeine has a lot of cognitive benefits. A researcher decides to investigate whether one drinks coffee or not will affect the number of correct answers one will get on a 50 question multiple choice exam. The researcher splits 12r subjects into two groups: one that drank coffee and one that did not before the exam. For the non-coffee group however one participant ate a bad mushroom the night before the exam and needed to drop out leaving only 5 in that group. Using the data presented below, does caffeine have an effect on the number of correct answers? Use alpha = 0.01 SS1 = 98.83 SS2 = 54Explanation / Answer
Hypotheses:
H0: muCoffee-muNon-coffee=0 (there is no difference in mean number of correct answers given by coffee and non-coffee drinkers)
H1:muCoffee-muNon-coffee=/=0 (there is a difference in mean number of correct answers given by coffee drinkers and non-coffee drinkers)
Assumptions: Independent group assumption: the researchers split 12 subjects in two groups randomly, therefore, th egroups are independent.
Independence assumption: the coffee drinkers is independent of non-coffee drinkers.
Randomization condition: the study is an experiment, where, comparison in correct answers is made among treatment and control group. Therefore, randomization condition is met.
Nearly normal condition: the histograms are not normal.
The t test is robust to normalization condition. The other assumptions being met, use 2-sample t test for difference in means.
Test statistic.
t=(xbar coffee-xbar non-coffee)/sqrt[s^2 coffee/n coffee+s^2 non-coffee/n non-coffee], where, xbar is sample mean, s is sample standard deviation, n is sample size. The computational formula for xbar is xbar=sigma x/n, standard deviation, s=sqrt[1/n-1 sigma (x-xbar)^2].
=(44.17-40)/sqrt[4.45^2/6+3.67^2/5]
=1.70
p value at 8 degrees of freedom is 0.127.
df=[(s1^2/n1+s2^2/n2)^2/{1/n1-1(s1^2/n1)^2+1/n2-1(s2^2/n2)^2}]
Conclusion: Reject H0, if p value is less than alpha=0.01. Here, p value is not less than 0.01. Therefore, fail to reject H0. There is insufficient sample evidence to conclude that there is a difference in mean number of correct answers given by coffee drinkers and non-coffee drinkers.
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