Final answer:
The 99% confidence interval for the population mean length of rainbow trout in Brainard Lake, Colorado, using the provided sample statistics, is approximately (10.07, 13.73) inches.
Step-by-step explanation:
To find a 99% confidence interval for the population mean length of all rainbow trout in Brainard Lake, Colorado, we can use the following formula for the confidence interval:
CI = μ ± (t* × (s / √n))
where:
- μ = sample mean
- t* = t-value from the t-distribution table corresponding to the 99% confidence level and degrees of freedom (n-1)
- s = sample standard deviation
- n = sample size
Given:
- μ = 11.9 inches
- s = 2.8 inches
- n = 19
We have to look up the t-value for a two-tailed test at a 99% confidence level with 18 degrees of freedom (19 - 1 = 18). Let's assume the t-value we find is approximately t* = 2.861.
Calculating the margin of error (ME):
ME = t* × (s / √n) = 2.861 × (2.8 / √19) ≈ 1.83
Now, applying it to the confidence interval formula:
CI = 11.9 ± 1.83
Therefore, the 99% confidence interval for the mean length of the rainbow trout in the lake is:
(10.07, 13.73) inches