Answer to Question #215365 in Statistics and Probability for ruby

Question

Instructor Ramos is concerned about the amount of time teachers spend each week doing

schoolwork at home. A simple random sample of 56 teachers had a mean of 8.0 hours per week

working at home after school. Construct and interpret a 95% confidence interval for the mean

number of hours per week a teacher spends working at home. Assume that the population

standard deviation is 1.5 hours per week.

Answer 1

$n=56 \\ \mu=8.0 \\ \sigma=1.5$

Two-sided confidence interval:

$CI = (\mu - \frac{Z_c \times \sigma}{\sqrt{n}}, \mu + \frac{Z_c \times \sigma}{\sqrt{n}}) \\ CI = (8.0 - \frac{1.96 \times 1.5}{\sqrt{56}}, 8.0 + \frac{1.96 \times 1.5}{\sqrt{56}}) \\ CI = (8.0 - 0.39, 8.0 + 0.39) \\ CI = (7.61, 8.39)$