Question

Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:
n_1 = 10 and x_1 = 87.6 sigma_1 = 1 and n_2 = 12 x^2 = 74.5 sigma_2 = 1.5. If mu_1 and mu_2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the .difference in mean strength.

Answer 1

Answer:

(12.1409, 14.0591

Step-by-step explanation:

Given that Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known.

Group   Group One     Group Two  

Mean 87.600 74.500

SD 1.000 1.500

SEM 0.316 0.433

N 10      12    

The mean of Group One minus Group Two equals 13.100

standard error of difference = 0.556

 90% confidence interval of this difference:  

$(13.1-1.725*0.556,13.1+1.725*0.556)\\=(12.1409, 14.0591)$

  t = 23.5520

 df = 20