The makers of the Liquid Braino® brand energy drink claim that their product con
ID: 3298703 • Letter: T
Question
The makers of the Liquid Braino® brand energy drink claim that their product contains special ingredients that can improve a person’s memory. To test this claim, a public interest organization randomly selected 12 individuals, and then randomly assigned each of these individuals to one of two possible groups:
i. The experimental group ("Braino Group"), in which each subject drank a case of Liquid Braino.
ii. The control group ("Placebo Group"), in which each subject drank a case of a soda that looked and tasted exactly like Liquid Braino, but did not contain any of Liquid Braino’s special ingredients.
(No subjects knew which type of drink they had been given.) Later, all subjects were given a memory test, in which higher scores indicate better memory. The scores earned by the subjects in each group are listed below:
Braino Group
Placebo Group
90
87
65
66
70
76
80
76
30
32
55
44
(Assume that the underlying populations are normally distributed, with equal variances.) Conduct the appropriate t-test, at a = .05, to determine whether drinking Liquid Braino can improve a person’s memory. Once again...MAKE SURE THAT YOU PICK THE CORRECT HYPOTHESIS TEST!
Start with the hypotheses and proceed through interpretation.
Braino Group
Placebo Group
90
87
65
66
70
76
80
76
30
32
55
44
(Assume that the underlying populations are normally distributed, with equal variances.) Conduct the appropriate t-test, at a = .05, to determine whether drinking Liquid Braino can improve a person’s memory. Once again...MAKE SURE THAT YOU PICK THE CORRECT HYPOTHESIS TEST!
Start with the hypotheses and proceed through interpretation.
Explanation / Answer
Null HYpothesis : H0 : drinking liquid braino doesn't improve a person's memory. BRaino Group = Placebo Group
ALternative HYpothesis : Drinking liquid braino does improve a person's memory. Ha : BRaino Group > Placebo Group
Brainy Group xbrainy = 65
Placebo Group xplacebo = 63.5
standard deviation sbrainy = 20.98
standard deviation splacebo = 21.18
Assume that the underlying populations are normally distributed, with equal variances.
Pooled standard deviation sp = sqrt [(nbrainy -1)s2brainy + (nplacebo -1) s2placebo / (nbrainy + nplacebo -2)]
sp = sqrt [ (5 * 20.982 + 5 * 21.182 ) / (10)] = 21.08
test statistic
t = (xbrainy - xplacebo)/ (sp * sqrt (1/nbrainy +1/nplacebo)
t = (65 - 63.5)/ 21.08 * sqrt (1/5 + 1/5) ]
t = 1.5/ 13.33 = 0.1125
at a = 0.05
Here, dF = 10
critical value of t => tcritical = 1.8125
so here t < tcritical , so we cannot reject the null hypothesis and can conclude that drinking liquid braino doesn't improve a person's memory. or Drinking liquid braino doesn't put effect on any person's memory.
Braino Placebo 90 87 65 66 70 76 80 76 30 32 55 44 average 65 63.5 Std. dev. 20.97618 21.18254Related Questions
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