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.

(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  

Mean87.60074.500

SD1.0001.500

SEM0.3160.433

N10      12    

The mean of Group One minus Group Two equals 13.100

standard error of difference = 0.556

 90% confidence interval of this difference:  

  t = 23.5520

 df = 20

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.