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Answer :
Final answer:
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.
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.
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