Solution:
x | (x-x̄ ) | (x-x̄ )^2 |
138 | 3.6 | 13.96 |
128 | -6.4 | 40.96 |
135 | 0.6 | 0.36 |
134 | -0.4 | 0.16 |
137 | 2.6 | 6.76 |
Sum of X= 672 | Sum of (x-x̄ )^2= 61.2 |
a)
Given that:
n = 5
Sample Mean x̄ = Sum of x/n
= 672/5
Sample mean x̄= 134.40
Sample standard deviation S= sqrt (sum of (x-x̄ )^2/n-1)
= sqrt (61.2/5-1)
=sqrt (61.2/4)
Sample standard deviation S= 1.9558
150 A.C. skull breadths mean = 134.40
150 A.C. Skull breadths standard deviation = 1.9558
b)
(1-α)%= 95%
1-α= 0.95
α= 0.05
α/2=0.025
t(α/2),(n-1)=t(0.025),(5-1)
=t(0.025),(4)= 2.776.... From students t table.
95% confidence interval for the population mean is given as,
x̄ - t(α/2),(n-1) ×( S / sqrt (n) ) , x̄ + t(α/2),(n-1) ×( S / sqrt
(n) )
134.40 - (2.776)×(1.9558/ sqrt (5)) , 134.40 +
(2.776)×(1.9558/ sqrt (5))
134.40 - 2.4281 , 134.40 + 2.4281
131.9719 , 136.8281
( 131.97 , 136.83)
95% confidence interval :
150 A. C. skull breadths : 131.97 to 136.83
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