Question

A beer company tested 4 bottles of its competitor's beer to see how many ounces were in each bottle. The results were: 11.7 , 11.8 , 12.1 , 11.8 ounces. Find a 99 % confidence interval for the mean number of ounces in each bottle.

Answer 1

We first need to calculate the mean and standard deviation of the number of ounces in the sample

	X	X2
	11.7	136.89
	11.8	139.24
	12.1	146.41
	11.8	139.24
Sum =	47.4	561.78

Mean = 11.85

Sample Variance = 0.03

Standard deviation, s = 0.173205

Since we don't know the population sigma, we need to find the critical t value for 99% confidence and 3 (4-1) degree of freedom, tc = 5.841

The confidence interval is calculated by

So, the 99% confidence interval for the mean number of ounces in each bottle is (11.344,12.356)

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