A market research company wishes to know how many energy drinks teenagers drink each week. They want to construct a 80%

Question

confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.9
. The study found that for a sample of 369
teenagers the mean number of energy drinks consumed per week is 5.7
. Construct the desired confidence interval. Round your answers to one decimal place.

Answer 1

To construct a confidence interval for the mean number of energy drinks consumed per week, we can use the formula:

Confidence interval = mean ± Z * (standard deviation / sqrt(n))

Where Z is the z-score corresponding to the desired confidence level. Since we want an 80% confidence interval, the z-score is 1.28.

Plugging in the values:

Confidence interval = 5.7 ± 1.28 * (0.9 / sqrt(369))
Confidence interval = 5.7 ± 1.28 * (0.9 / 19.2)
Confidence interval = 5.7 ± 0.06
Confidence interval = (5.64, 5.76)

Therefore, the 80% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.64, 5.76).