Answer:
Point estimate for the population standard deviation = 0.048
Step-by-step explanation:
We are given that a sample of 6 sewing needles is randomly selected and the following diameters are measured in millimeters;
X X - X bar [tex](X-Xbar)^{2}[/tex]
0.95 0.95 - 1.005 = -0.055 0.003025
0.99 0.99 - 1.005 = -0.015 0.000225
1.04 1.04 - 1.005 = 0.035 0.001225
0.95 0.95 - 1.005 = -0.055 0.003025
1.05 1.05 - 1.005 = 0.045 0.002025
1.05 1.05 - 1.005 = 0.045 0.002025
Total = 0.01155
Firstly, mean of the data above, X bar = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{6.03}{6}[/tex] = 1.005
Standard deviation of data, S.D. = [tex]\sqrt{\frac{\sum (X-Xbar)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{0.01155}{6-1} }[/tex] = 0.048
Therefore, point estimate for the population standard deviation is 0.048 .
