Questions: Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 16 boxes. It is reasonable to assume that the population is approximately normal. 14.07, 13.98, 14.16, 14.17, 14.11, 14.03, 14.16, 13.98, 14.06, 14.05, 14.12, 14.13, 14.19, 14.17, 14.05, 14.04, Send data to Excel Part: 0 / 2 Part 1 of 2 (a) Construct a 95% confidence interval for the mean weight. Round the answers to at least three decimal places. A 95% confidence interval for the mean weight is <μ< .

Solution Steps

The mean weight of the cereal boxes is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{225.47}{16} = 14.092 \]

The variance is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 0.005 \]

Thus, the sample standard deviation is:

\[ \sigma = \sqrt{0.005} = 0.068 \]

For a 95% confidence level, the Z-score is \( Z = 1.96 \). The margin of error is calculated as:

\[ \text{Margin of Error} = \frac{Z \times \sigma}{\sqrt{n}} = \frac{1.96 \times 0.068}{\sqrt{16}} = 0.033 \]

The 95% confidence interval for the mean weight is given by:

\[ \text{Lower Bound} = \mu - \text{Margin of Error} = 14.092 - 0.033 = 14.059 \]

\[ \text{Upper Bound} = \mu + \text{Margin of Error} = 14.092 + 0.033 = 14.125 \]

Thus, the confidence interval is:

\[ 14.059 < \mu < 14.125 \]

Final Answer