Question 1204252
p1 = 960/1000 = .96
p2 = 582/600 = .97
average of p1 + p2 = (960 + 582) / (1000 + 600) = .96375
call that p0.
standard error = sqrt((p0 * (1-p0) * (1/1000 + 1/600)) = .009652
z-score = (.96 - .97) / .009652 = -1.036055
area to the left of that = .150088
that's the test p-value on the left of the confidence interval.
same area ia on the right for a total test p-value of .300176.
critical p-value is .01.
since the test p-value is greater than the critical p-value, the results are not significant.
the conclusion is that there is not enough evidence to show that the two samples are not equally effectivfe at meeting the specifications.
this means that they can be considered to be equally effective at producing rods that meet the specifications.
online calculator gives the same results plus or minus a few because of rounding, as shown below.


<img src = "http://theo.x10hosting.com/2023/101501.jpg">


here's a reference.


<a href = "https://sixsigmastudyguide.com/two-sample-test-of-proportions/#:~:text=Two%20sample%20Z%20test%20of%20proportions%20is%20the%20test%20to,that%20have%20some%20single%20characteristic." target = "_blank">https://sixsigmastudyguide.com/two-sample-test-of-proportions/#:~:text=Two%20sample%20Z%20test%20of%20proportions%20is%20the%20test%20to,that%20have%20some%20single%20characteristic.</a>