Two alloys A and B are being used to manufacture a certain steel product. An experiment needs to be designed to compare the two in terms of maximum load capacity in tons (the maximum weight that can be tolerated without breaking). It is known that the two standard deviations in load capacity are equal at 5 tons each. An experiment is conducted in which 30 specimens of each alloy (A and B) are tested and the results recorded as follows: x¯A = 49.5, x¯B = 45.5, x¯A − x¯B = 4
The manufacturers of alloy A are convinced that this evidence shows conclusively that muA & muB and strongly supports the claim that their alloy is superior. Manufacturers of alloy BB claim that the experiment could easily have given x¯A − x¯B = 4 even if the two population means are equal. In other words, "the results are inconclusive!"
(a) Make an argument that manufacturers of alloy B are wrong. Do it by computing
P(x¯A − x¯B > 4 | muA - muB
(b) Do you think these data strongly support alloy A?

Step-by-step explanation:

From the given information, we can compute the table showing the summarized statistics of the two alloys A & B:

                                            Alloy A        Alloy B

Sample mean                          

Equal standard deviation            

Sample size                                  

Mean of the sampling distribution is :

Standard deviation of sampling distribution:

Hypothesis testing.

Null hypothesis:  

Alternative hypothesis:  

The required probability is:

This implies that a minimal chance of probability shows that the difference of 4 is not likely, provided that the two population means are the same.

b)

Since the P-value is very small which is lower than any level of significance.

Then, we reject and conclude that there is enough evidence to fully support alloy A.

a negative exponent is translated as follows:

so, we have

step-by-step explanation:

this is not possible to solve with the info given.   you need at least an one angle somewhere.