Example 10-6 ? A quality inspector counted the number of...

Example 10-6 ? A quality inspector counted the number of defective parts a prototype machine made in samples of 100 taken every hour during a 20-hour period. a) Using the following data, construct a Three Sigma control chart for the sample proportion of defectives. b) Is the machine producing a stable proportion of defectives?

Transcript

00:01 Hello student, as per the given problem first we will note down the given info.

00:05 So we are provided with a total sample size n to be 100, number of chips from the operation a in the sample, number of chips from the operation b in the sample, number of defective chips in the operation a and b respective.

00:19 So first as per the question we have to solve the problem by simple random sample estimate.

00:25 So to estimate the proportion of defective in the lot using a simple random sample we can use the sample.

00:32 By using the given information first we will calculate the p hat total.

00:37 So formula for p hat total is equal to total defective chips in the sample divided by total sample.

01:07 Now we will plug in value here and it becomes total defective chips in the sample is equal to 6 plus 10 divided by 100.

01:16 So it comes out to be 0 .16.

01:18 So we can say that p hat total is 0 .16.

01:23 So the estimated proportion of defective in the lot is 0 .16.

01:28 Next bound on the error of error.

01:31 So to place the bound of error we can calculate the confidence interval for the proportion using the confidence level.

01:43 For that we can use the formula margin of error is equal to z into under root of p hat total multiplied by 1 minus p hat total divided by n.

02:00 Now z is the critical value which we can calculate by the desired confidence.

02:06 Here it is given to be 95 percent.

02:11 So our z come out to be 1 .96 into under root of 0 .16 into 0 .84 divided by 100...

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