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Question:
The amounts (in ounces) of randomly selected eight 16-ounce beverage cans are given below.
16.5, 15.2, 15.4, 15.1, 15.3, 15.4, 16, 15.1
Assume that the amount of beverage in a randomly selected 16-ounce beverage can has a normal distribution. Compute a 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans and fill in the blanks appropriately.
A 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is ( , ) ounces. (round to 3 decimal places)
Answer:
Therefore, the 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (14.886, 16.113) ounces.
Step-by-step explanation:
Let us find out the mean amount of the 16-ounce beverage cans from the given data.
Using Excel,
=AVERAGE(number1, number2,....)
The mean is found to be
Let us find out the standard deviation of the 16-ounce beverage cans from the given data.
Using Excel,
=STDEV(number1, number2,....)
The standard deviation is found to be
The confidence interval is given by
Where is the sample mean and Margin of error is given by
Where n is the sample size, s is the sample standard deviation and is the t-score corresponding to a 99% confidence level.
The t-score corresponding to a 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 8 - 1 = 7
From the t-table at α = 0.005 and DoF = 7
t-score = 3.4994
So the required 99% confidence interval is
Therefore, the 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (14.886, 16.113) ounces.
