Question

mechanical engineer wishes to compare strength properties of steel beams with similar beams made with a particular alloy. The same number of beams, n, of each type will be tested. Each beam will be set in a horizontal position with a support on each end, a force of 2500 lb will be applied at the center, and the deflection will be measured. From past experience with such beams, the engineer is willing to assume that the true standard deviation of deflection for both types of beam is 0.06 in. Because the alloy is more expensive, the engineer wishes to test at level 0.01 whether it has smaller average deflection than the steel beam. What value of n is appropriate if the desired type 11 error probability is 0.05 when the difference in true average deflection favors the alloy by 0.05 in. (Round your answer up to the next whole number) X beams

Answer 1

Answer:

Given,

Ho : u1 = u2

Ha : u1 > u2

$\beta$($\Delta$') = $\Phi$ (z(alpha) - ($\Delta$'-$\Delta$o)/$\sigma$)

1.645 = 2.33 - (($\Delta$'-$\Delta$o)/$\sigma$)

1.645 = 2.33 - (0.05 - 0)/$\sigma$

$\sigma$^2 = 0.05^2/(1.645 + 2.33)^2

$\sigma$^2 = 0.000158

Consider,

Variance = $\sigma$ 1^2/n1 + $\sigma$ 2^2/n2

substitute values

$\sigma$^2 = (0.06^2/n) + (0.06^2/n)

= 0.0072/n

Now,

substitute $\sigma$ ^2 = 0.005 , so

0.0072/n = 0.000158

n = 45.5696

n = 46