The following sample data are from a normal population: 20, 24, 27, 26, 23 a. Wh
ID: 3360390 • Letter: T
Question
The following sample data are from a normal population: 20, 24, 27, 26, 23 a. What is the point estimate of the population mean? b What is the point estimate of the population standard deviation to 3 decimals)? C. Develop a 90% confidence interval for the population mean (to 3 decimals). d. Develop a 95% confidence interval for the population mean (to 3 decimals). e. Develop a 99% confidence interval for the population mean (to 3 decimals). f. What happens to the margin of error and the confidence interval as the confidence level isi 0 A. Error increases and interval narrows O B. Error increases and interval widens O C. Error decreases and interval widens 0 D. Error decreases and interval narrows
Explanation / Answer
A) point estimate of population mean = (20 + 24 + 27 + 26 + 23)/5 = 24
B) population variance = ((20 - 24)^2 + (24 - 24)^2 + (27 - 24)^2 + (26 - 24)^2 + (23 - 24)^2)/5 = 6
Population standard deviation = sqrt(6) = 2.45
Point estimate of population standard deviation = 2.45/sqrt(5) = 1.096
C) At 90% confidence interval the critical value is Z0.95 = 1.645
Mean +/- Z0.95 * SD/sqrt (n)
= 24 +/- 1.645 * 1.096
= 24 +/- 1.803
= 22.197, 25.803
D) At 95% cinfidence interval the critical value is Z0.975 = 1.96
Confidence interval is
Mean +/- Z0.975 * SD/sqrt (n )
= 24 +/- 1.96 * 1.096
= 24 +/- 2.148
= 21.852, 26.148
E) At 99% cinfidence interval the critical value is Z0.995 = 2.58
Cinfidence interval is
Mean +/- Z0.995 * SD/sqrt (n )
= 24 +/- 2.58 * 1.096
= 24 +/- 2.828
= 21.172, 26.828
F) Option-B