Answer:
(a) Point estimate of the population mean = 10
(b) Point estimate of the population standard deviation = 3.21
(c) The margin of error for the estimation of the population mean = 2.2
(d) 95% confidence interval for the population mean = [7.8 , 12.2] .
Step-by-step explanation:
Arranging our sample data given from a normal population in ascending order we get ; 5+ 6+ 9+ 10+ 11+ 12+ 13+ 14
(a) Point estimate of population mean is given by Xbar;
Xbar = where n = 8 {number of obs. in data}
Xbar = = 10
(b) Point estimate of the population standard deviation is given by ;
Standard deviation formula =
Solving above formula we get point estimate of the population standard deviation = 3.21 .
(c) Margin of error for the estimation of the population mean is given by the expression ;
95% Confidence Interval for population mean = Xbar Margin of error
where <em>Margin of error = 1.96 * </em> {Here 1.96 is written because at 5% level
of significance z table has a value of 1.96
for two tail}
Therefore, Margin of error = = 2.2
(d) 95% Confidence Interval for population mean = Xbar 1.96 *
= 10 = 10 2.2
= [10 - 2.2 , 10 + 2.2]
Therefore, 95% C.I. for population mean = [7.8 , 12.2] .