Question

and the standard normal table to find a 95% two-sided confidence interval on mean. 3. By using a statistical software, namely MATLAB, the random sample from a normal distribution is generated as given below: 9.11 9.55 10.30 9.39 10.49 10.73 12.77 9.80 7.86 a) (10 Points) Calculate the sample mean and sample variance. b) (10 Points) Find a 95% two-sided confidence interval on mean. Provide a practical interpretation of this interval c) (10 Points) Find a two-sided confidence interval on mean at significance level a = 0.01. Provide a practical interpretation of this interval.

Answer 1

a)

	X	(X - X̄)²
total sum	90	14.52
n	9	9

mean =    ΣX/n =    90/9=   10.000
sample variance =    Σ(X - X̄)²/(n-1)=   14.5222/8=   1.8153

b)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   1.3473
Sample Size ,   n =    9
Sample Mean,    x̅ = ΣX/n =    10.0000
Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   8          
't value='   tα/2=   2.306   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   1.3473/√9=   0.4491          
margin of error , E=t*SE =   2.3060   *   0.4491   =   1.036
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    10.00   -   1.0356   =   8.9644
Interval Upper Limit = x̅ + E =    10.00   -   1.0356   =   11.0356
95%   confidence interval is (   8.964   < µ <   11.036   )

we are 95% confident that true popualtion mean will lie between (8.964 , 11.036)

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c)

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   8          
't value='   tα/2=   3.355   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   1.3473/√9=   0.4491          
margin of error , E=t*SE =   3.3554   *   0.4491   =   1.507
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    10.00   -   1.5069   =   8.4931
Interval Upper Limit = x̅ + E =    10.00   -   1.5069   =   11.5069
99%   confidence interval is (   8.493   < µ <   11.507   )

we are 99% confident that true popualtion mean will lie between (8.493 , 11.507)

...................

thanks

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