Question

Fernando wants to estimate the average caloric content of his smoothies. He obtains a random sample of 14 smoothies and measures their caloric content. The sample data is roughly symmetric with a mean of 250 calories with a standard deviation of 20 calories. Based on this sample, what is the 95% confidence interval for the mean caloric content of the smoothies? 3

Answer 1

To estimate the average caloric content of Fernando's smoothies, we can construct a 95% confidence interval using the sample mean, standard deviation, and sample size. The confidence interval is approximately 237.99 to 262.01 calories.

Step-by-step explanation:

To construct a 95% confidence interval for the mean caloric content of the smoothies, we can use the formula:

Confidence Interval = mean ± (z * standard deviation / sqrt(sample size))

Given that the mean is 250 calories, the standard deviation is 20 calories, and the sample size is 14, we need to find the z-value for a 95% confidence level. The z-value for a 95% confidence level is approximately 1.96.

Substituting the values into the formula, we get:

Confidence Interval = 250 ± (1.96 * 20 / sqrt(14))

Simplifying the expression gives us a 95% confidence interval of approximately 237.99 to 262.01 calories