Question
A market research company wishes to know how many energy drinks teenagers drink each week. They want to construct a 80%
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.
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.
Answers
GPT 3.5
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).
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).