The piston diameter of a certain hand pump is
0.5
inch. The manager determines that the diameters are normally distributed, with a mean of
0.5
inch and a standard deviation of
0.003
inch. After recalibrating the production machine, the manager randomly selects
24
pistons and determines that the standard deviation is
0.0022
inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the
α=0.01
level of significance?
mean = µ = 0.5 inch standard deviation = σ = 0.003 inch
n = 24 , s = 0.0022 inch
Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α =0.01
Ho: σ ≥ 0.003
Ha : σ < 0.03
level of significance = α = 0.01
Degree of freedom = n - 1 = 23
Test statistic = X^2 = (n-1)s^2/σ^2 = (24-1)0.0022^2/0.003^2 = 12.369
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