Final answer:
To construct a 99% confidence interval for the population mean, use the t-distribution to find the critical value, calculate the margin of error, and add and subtract this margin from the sample mean.
Step-by-step explanation:
To construct a 99% confidence interval for the population mean μ, with a sample mean ᵐ = 11.9, sample size n = 14, and sample standard deviation s = 2, we must use the t-distribution because the population standard deviation is unknown and the sample size is small.
First, determine the critical value (t*) for 99% confidence using a t-table or statistical software, since n = 14, the degrees of freedom we use is n - 1 = 13. Once you have t*, calculate the margin of error as E = t* × s / √n. Finally, construct the interval by adding and subtracting the margin of error from the sample mean: Interval = (ᵐ - E, ᵐ + E).
To construct a 99% confidence interval for the population mean, we will use the formula: x ± z * (s / sqrt(n)), where x is the sample mean, s is the sample standard deviation, and n is the sample size. The z value represents the desired level of confidence and can be found in the Z-table. For a 99% confidence interval, the z value is approximately 2.58.
Substituting the given values, we have: 11.9 ± 2.58 * (2 / sqrt(14)). Calculating this expression, we get the confidence interval (10.064, 13.736) for the population mean μ.