High energy: A random sample of energy drinks had the following amounts of caffe

Question

High energy: A random sample of energy drinks had the following amounts of caffeine per fluid ounce 14.2 83 80.8 6.7 3.6 13.7 12.9 11.5 24.7 9..5 Assume the population standard deviation is ?-24. a. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval. b. Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal? 90 0 10 20 30 40 50 60 70 80 90 C. If appropriate, construct a 95% confidence interval for the mean amount of caffeine in all energy drinks. If not appropriate, explain why not.

Explanation / Answer

a)

Here it is not given that population is normally distributed and sample size is less than 30 so it is necessary to check whether the population is approximately normal before constructing the confidence interval.

b)

Dot plot shows that the distribution is skewed to right and it has high outlier also. So it is not reasonable to assume that the population is approximately normal.

c)

Since normallity cannot be assumed so it is not appropriate to construct the confidence interval.

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