Question

A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 98%

confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.3
. The study found that for a sample of 1133
adults the mean number of energy drinks consumed per week is 7.1
. Construct the desired confidence interval. Round your answers to one decimal place.

Answer 1

The 98% confidence interval for the mean number of energy drinks consumed by adults each week, with a population standard deviation of 1.3 and a sample mean of 7.1 from a sample size of 1133, is between 7.02 and 7.18.

Step-by-step explanation:

The question revolves around constructing a 98% confidence interval for the mean number of energy drinks consumed by adults each week. Given that the population standard deviation (σ) is 1.3, the sample mean (μ) is 7.1, and the sample size (n) is 1133, we can calculate the confidence interval using the z-score for a 98% confidence level.

First, we find the z-score that corresponds to a 98% confidence level, which is approximately 2.33 (using a z-table). Next, the formula for the confidence interval is:

CI = μ ± (z * (σ/√n))

1. Calculate the margin of error: Margin of error (E) = z * (σ/√n) = 2.33 * (1.3/√1133) ≈ 0.08
2. Construct the confidence interval: CI = 7.1 ± 0.08, which gives us (7.02, 7.18).

Therefore, we are 98% confident that the true mean number of energy drinks consumed per week by adults is between 7.02 and 7.18.