Final answer:
a. The point estimate of the population mean is 10.875. b. The point estimate of the population standard deviation is approximately 3.906. c. The margin of error for the estimation of the population mean is approximately 2.261.
Step-by-step explanation:
a. The point estimate of the population mean is equal to the sample mean. In this case, the sample mean is 11 + 9 + 13 + 16 + 14 + 12 + 7 + 6 divided by 8, which equals 10.875. So, the point estimate of the population mean is 10.875.
b. The point estimate of the population standard deviation is equal to the sample standard deviation. In this case, the sample standard deviation can be calculated using the formula: square root of [ (11-10.875)^2 + (9-10.875)^2 + (13-10.875)^2 + (16-10.875)^2 + (14-10.875)^2 + (12-10.875)^2 + (7-10.875)^2 + (6-10.875)^2 divided by (8-1) ]. After calculating, the sample standard deviation is approximately 3.906.
c. The margin of error for the estimation of the population mean can be calculated using the formula: t * (sample standard deviation / square root of sample size), where t is the critical value for a 95% confidence interval with (n-1) degrees of freedom. Since the sample size is 8, the degrees of freedom is 8-1 = 7. The critical value for a 95% confidence interval with 7 degrees of freedom can be found using a t-distribution table or a statistical calculator. Let's assume the critical value is 2.365. Plugging the values into the formula, the margin of error is approximately 2.365 * (3.906 / square root of 8), which is approximately 2.261.