A nonprofit organization commissions a study to find the average cost of a college textbook. After looking at 121 textbooks, it finds that the average cost is $52.00, with a standard deviation of $5.50. What is the 95% confidence interval for the average cost of a college textbook?
To calculate the 95% confidence interval for the average cost of a college textbook, we can use the formula:
Confidence Interval = X̄ ± Z * (σ / √n)
Where:
X̄ = sample mean ($52.00)
Z = Z-score for 95% confidence interval (1.96)
σ = standard deviation ($5.50)
n = sample size (121)
Plugging in the values:
Confidence Interval = $52.00 ± 1.96 * ($5.50 / √121)
Confidence Interval = $52.00 ± 1.96 * ($0.50)
Confidence Interval = $52.00 ± $0.98
Therefore, the 95% confidence interval for the average cost of a college textbook is $51.02 to $52.98.