Recently energy drinks containing guarana have become increasingly popular in th
ID: 3157449 • Letter: R
Question
Recently energy drinks containing guarana have become increasingly popular in the U.S. Guarana is a creeping shrub native to Venezuela and northern Brazil. The fruit are small, bright red and contain black seeds. Guarana seeds are rich in caffeine and contain about four times more than coffee beans. They are also rich in tannins and xanthine alkaloids. Guarana is reputed to be a stimulant and increase mental alertness, fight fatigue, and increase stamina and physical endurance. To test guaranas effect on memory, a standard computer test of memory was utilized. This test has a mean score of 90 for the thousands of people who have taken it on line. A random sample of 25 college sophomores were given 12 oz drinks of Kuat, a drink produced by the Coca-Cola Company for the Brazilian market. Kuat has high levels of guarana and 82 calories per 200ml serving. The students waited 30 minutes, then took the computerized memory test. The results were: X = 93:5 points and s2 = 36 points. Did the Kuat significantly increase memory scores?
Explanation / Answer
As significance level is not given, we set it to 0.05.
Formulating the null and alternative hypotheses,
Ho: u <= 90
Ha: u > 90
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 24
tcrit = + 1.71088208
Getting the test statistic, as
X = sample mean = 93.5
uo = hypothesized mean = 90
n = sample size = 25
s = standard deviation = 6
Thus, t = (X - uo) * sqrt(n) / s = 2.916666667
Also, the p value is
p = 0.003778972
As t > 1.711, and P < 0.05, we REJECT THE NULL HYPOTHESIS.
Hence, Kuat significantly increase memory scores. [CONCLUSION]
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