A market research company wishes to know how many energy drinks adults 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 164 adults the mean number of energy drinks consumed per week is 7.9 . Construct the desired confidence interval. Round your answers to one decimal place. AnswerHow to enter your answer (opens in new window) 2 Points Keypad Lower endpoint:

To construct the \( 80\% \) confidence interval for the mean number of energy drinks consumed per week, we can use the formula: \[ \text{Confidence Interval} = \bar{x} \pm z \cdot \left(\frac{\sigma}{\sqrt{n}}\right) \] Where: - \(\bar{x} = 7.9\) (sample mean), - \(\sigma = 0.9\) (population standard deviation), - \(n = 164\) (sample size), - \(z\) is the z-score corresponding to the desired confidence level. For an \(80\%\) confidence interval, the z-score is approximately \(1.28\). Now, calculating the margin of error: 1. Find the standard error (SE): \[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.9}{\sqrt{164}} \approx \frac{0.9}{12.81} \approx 0.0704 \] 2. Compute the margin of error (ME): \[ ME = z \cdot SE = 1.28 \cdot 0.0704 \approx 0.0902 \] Now, calculate the confidence interval: Lower endpoint: \[ 7.9 - 0.0902 \approx 7.8 \] Upper endpoint: \[ 7.9 + 0.0902 \approx 7.99 \approx 8.0 \] Thus, rounding to one decimal place, the confidence interval is approximately: Lower endpoint: **7.8** Upper endpoint: **8.0**