Two processes in a manufacturing line are performed manually...

Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 50 different assemblies using operation A shows that the sample average time per assembly is 8.05 minutes, with a population standard deviation of 1.36 minutes. A random sample of 38 different assemblies using operation B shows that the sample average time per assembly is 7.26 minutes, with a population standard deviation of 1.06 minutes. For α=.10, is there enough evidence in these samples to declare that operation A takes significantly longer to perform than operation B? Find the z-score to make a conclusion. Round the answer to two decimal places.

Transcript

00:01 In this video, we are going to focus on finding out the value of test statistics based on the given information about a manufacturing line in which there are two processes.

00:09 So first process is named as operation a and the second process is named as operation b.

00:15 So here we can say that we have some information such as we have the sample size for 1 that is a to be equals to 50 and then we have the sample size for b to be equal to 50.

00:30 To here as 38 and then here we have the information that x1 or we can say xa value is equals to here as 8 .05 and then here we have the information that xb value will be here equals to 7 .26.

00:51 Now it is basically we can say xb bar and this one is xa bar.

00:56 Now let us write the hypothesis.

00:59 So, hypothesis, that is null hypothesis, will be that mu1 is equals to mu 2, and alternate hypothesis will be here that mu 1 is greater than mu 2.

01:11 So, here, based on the given information, we can here write that the value of test statistic will be here equals to x1, or we can say xa bar, and it will be here minus xb bar, and then in the denominator we are going to have under root of, it will be sigma 1.

01:32 So we have the sigma value as well.

01:34 So we can write the sigma a value over here.

01:37 And this is equals to 1 .36.

01:41 And sigma b value is equals to, we can say, 1 .06.

01:47 So sigma a square divided by n1 or n .a, we can write it.

01:52 And then it will be here, sigma b square.

01:55 And then in the denominator we have n2...