Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 14 boxes. It is reasonable to assume that the population is approximately normal.14.07 13.99 14.16 14.17 14.15 14.11 14.2413.99 14.14 14.13 14.20 14.21 14.06 14.05Send data to ExcelPart: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Construct a 99.9% confidence interval for the mean weight. Round the answers to at least three decimal places.A 99.9% confidence interval for the mean weight is <<μ.
Question
Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 14 boxes. It is reasonable to assume that the population is approximately normal.14.07 13.99 14.16 14.17 14.15 14.11 14.2413.99 14.14 14.13 14.20 14.21 14.06 14.05Send data to ExcelPart: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Construct a 99.9% confidence interval for the mean weight. Round the answers to at least three decimal places.A 99.9% confidence interval for the mean weight is <<μ.
Solution
To construct a 99.9% confidence interval for the mean weight, we first need to calculate the mean and standard deviation of the sample data.
Here are the steps:
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Calculate the mean (average) of the sample data. Add up all the weights and divide by the number of weights.
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Calculate the standard deviation. This involves subtracting the mean from each weight, squaring the result, adding up these squares, dividing by the number of weights minus 1, and then taking the square root of that result.
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Determine the z-score for a 99.9% confidence interval. This is the number of standard deviations away from the mean that you need to go to capture 99.9% of the data in a normal distribution. The z-score for a 99.9% confidence interval is approximately 3.29.
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Calculate the standard error by dividing the standard deviation by the square root of the number of weights.
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Multiply the z-score by the standard error to get the margin of error.
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Subtract the margin of error from the mean to get the lower limit of the confidence interval and add the margin of error to the mean to get the upper limit of the confidence interval.
After performing these calculations, you will have a 99.9% confidence interval for the mean weight.
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