Given : Sample size n=140, sample mean m = 105 and sample standard deviation s=9
We have to find 95% confidence interval for population mean which is given by
(m - Margin of error ) ≤ μ ≤ (m + Margin of error)
Where Margin of error is given by
Margin of error =[tex] \frac{s*t}{\sqrt{n}} [/tex]
Where t = t critical value at alpha/2 level of significance and (n-1) degrees of freedom
Here alpha = 1- c = 1-0.95 = 0.05
degrees of freedom = n-1 = 140-1 = 139
Here we will use excel function to find t critical value which is
T.INV.2T(0.05, 139) = 1.977
The margin of error will be
ME = [tex] \frac{9 * 1.977}{\sqrt{140}} [/tex]
ME = 1.5
The 95% confidence interval will become
(105 - 1.5 , 105 + 1.5)
(103.5, 106.5)
So the correct answer option is option C. (103.5, 106.5)
Answer:
103.5–106.5
Step-by-step explanation:
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