Final answer:
a. The point estimate of the population mean is 10. b. The point estimate of the population standard deviation is 3.08. c. The margin of error for the estimation of the population mean is 2.58. d. The 95% confidence interval for the population mean is (7.4, 12.6).
Step-by-step explanation:
a. The point estimate of the population mean can be found by taking the average of the sample data. The sample data includes: 10, 8, 12, 15, 13, 11, 6, 5. The point estimate is the sample mean which is the sum of the data divided by the number of data points: (10+8+12+15+13+11+6+5)/8 = 10.
b. To estimate the population standard deviation, we can use the sample standard deviation, which is a measure of the variability of the sample data. The sample standard deviation can be calculated using the formula: sqrt(((10-10)^2+(8-10)^2+(12-10)^2+(15-10)^2+(13-10)^2+(11-10)^2+(6-10)^2+(5-10)^2)/(8-1)) = 3.08 (rounded to 2 decimal places).
c. The margin of error for the estimation of the population mean can be calculated using the formula: margin of error = critical value * standard error. Since we want a 95% confidence level, the critical value can be found using a t-distribution table or a calculator. For 95% confidence and 7 degrees of freedom (8-1), the critical value is approximately 2.365. The standard error can be calculated as the sample standard deviation divided by the square root of the sample size: 3.08/sqrt(8) = 1.09 (rounded to 1 decimal place). The margin of error is therefore 2.365 * 1.09 = 2.58 (rounded to 1 decimal place).
d. The 95% confidence interval for the population mean can be calculated by subtracting the margin of error from the sample mean (10 - 2.6) and adding the margin of error to the sample mean (10 + 2.6). The 95% confidence interval is therefore (7.4, 12.6) (rounded to 1 decimal place).