Answer:
Cl = (11.44, 16.96)
Explanation:
The formula to calculate the confidence interval for the population mean using the t-distribution is:
CI = x ± t_(α/2, n-1) * (s/√n)
Where CI is the confidence interval, x is the sample mean, s is the sample standard deviation, n is the sample size, t_(α/2, n-1) is the t-value with (n-1) degrees of freedom and a level of significance of α/2.
Given, C = 0.90, n = 10, x = 13.7, and s = 3.0.
The level of significance for a two-tailed test with a confidence level of 0.90 is 1 - C = 1 - 0.90 = 0.10. Therefore, α/2 = 0.10/2 = 0.05.
Using a t-distribution table with 9 degrees of freedom and a probability of 0.05, we find that t_(α/2, n-1) = 2.262.
Substituting the values into the formula, we get:
CI = 13.7 ± 2.262 * (3.0/√10)
= 13.7 ± 2.260
= (11.44, 16.96)
Therefore, the 90% confidence interval for the population mean is (11.44, 16.96).