Answer:
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:
![P(\overline X_A - \overline X_B>4|\mu_A - \mu_B) = P\Big (((\overline X_A - \overline X_B)-\mu_(X_A-X_B))/(\sigma_(\overline x_A -\overline x_B)) > (4 - \mu_(X_A-\overline X_B))/(\sigma _(\overline x_A - \overline X_B)) \Big) \\ \\ = P \Big( z > (4-0)/(1.2909)\Big) \\ \\ = P(z \ge 3.10)\\ \\ = 1 - P(z < 3.10) \\ \\ \text{Using EXCEL Function:} \\ \\ = 1 - [NORMDIST(3.10)] \\ \\ = 1- 0.999032 \\ \\ 0.000968 \\ \\ \simeq 0.0010](https://img.qammunity.org/2022/formulas/mathematics/college/aoh7fw25syombemofu0cg7bb6fvfm9scr0.png)
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.