To construct the 90% confidence interval, we will use the formula:
CI = x̄ ± Zα/2 * (σ/√n)
where:
- x̄ = sample mean = 15 hours
- Zα/2 = z-score for a 90% confidence interval = 1.645
- σ = population standard deviation = 2.5 hours
- n = sample size = 73
Plugging in the values:
CI = 15 ± 1.645 * (2.5/√73)
CI = 15 ± 1.645 * (2.5/8.544)
CI = 15 ± 1.645 * 0.293
CI = 15 ± 0.481
CI = (14.52, 15.48)
Therefore, the 90% confidence interval for the mean number of hours a student studies per week is (14.52, 15.48).
A professor wants to estimate how many hours per week her students study. A simple random sample of 73
students had a mean of 15
hours of studying per week. Construct a 90%
confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2.5
hours per week. Round to two decimal places.
1 answer