Question

A random sample of 31 eight-ounce servings of different juice drinks has a mean of 99.3 calories and a standard deviation of 41.5 calories. Interpret a 90% confidence interval for the mean number of calories in a juice drink:

Answer 1

A confidence interval is a range of values used to estimate the true value of a population parameter with a certain level of confidence. For this problem, a 90% confidence interval is used to estimate the mean number of calories in a juice drink.

Step-by-step explanation:

A confidence interval is a range of values that is used to estimate the true value of a population parameter with a certain level of confidence. In this case, a 90% confidence interval is being used to estimate the mean number of calories in a juice drink.

To calculate the 90% confidence interval, you can use the formula:

CI = X ± Z * (SD / √n)

Where:

- X is the sample mean (99.3 calories)

- Z is the Z-score for a 90% confidence level (1.645)

- SD is the standard deviation of the sample (41.5 calories)

- n is the sample size (31)

Plugging in the given values, the 90% confidence interval for the mean number of calories in a juice drink is:

CI = 99.3 ± 1.645 * (41.5 / √31)

CI = 99.3 ± 9.098

So the 90% confidence interval for the mean number of calories in a juice drink is approximately 90.202 to 108.398 calories.