Quarters. In Exercises 9–12, refer to the accompanying table o...

Question

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Quarters: xbar Chart Treat the 5 measurements from each day as a sample and construct an xbar chart. What does the result suggest?

Accepted Answer

All right, hello, everyone. So this question says, a manufacturing company produces rechargeable batteries and their lifespan is tested over multiple production days. The company collects 5 lifespan measurements in hours each day for quality control purposes. The following table represents the collected data. Treat the 5 measurements from each day as a sample and construct an X-bar chart. What does the result suggest? User provided control limits with X bar equal to 5.5 hours. The lower control limit or LCL is equal to 5.4 hours, and the upper control limit or UCL is equal to 5.7 hours. We're also given a blank chart for reference. All right, so let's begin with setting the X and Y axis of our chart, right? In this particular case, the X axis is going to represent each day in production. Whereas y is going to represent the mean. Of the sample So first, let's begin with plotting out the lower control limit and upper control limit. And I'm also going to create a key on the right side here. So in black, Are we drawing out the lower control limit? And then in orange, I'll be drawing out the upper control of it. So starting off with the upper control limit, that's set at 5.7 hours. So here, for each day towards the top, there's going to be a point at 5.7 date or hours, excuse me. And now that I have all the points on the graph, I'm going to go ahead and connect them with a line in between. And so now we do the same with the lower control limit. The lower control limit is going to be 5.4 hours. So there would be a dot at 5.4 for each of the days. All right, so now that we have the control limits, now let's go ahead and plot the daily sample mean for each of the 5 days. And going back to the data table that we were presented with, you'll notice that the sample mean or X bar. Was already given towards the very right side of the table for each day. So that's what we're going to be plotting in the X bar chart. So for the first day The sample mean was 5.5, so that's where the first point is going to go. For the second day it was 5.6 hours. For the third day was 5.4. For the 4th day it would be 5.7. And then for the 5th day, it would be at 5.5. So now each of the blue points. Would be connected once again with a line in between them. All right, so now let's talk about the interpretation of the export chart, now that it's complete. Well, in this case, the X-bar chart shows us the sample means for each day, along with both the upper and lower control limits. And what you'll notice here is that all of the data points, that is all of the points in blue, actually are within the control limits, right? Not only is it within the control limits, there's also no clear pattern indicating a trend or a shift. So therefore, the process appears to be in control, which means that the weights of the samples are consistent over time, with no significant variations beyond the expected randomness from one day to another. And so at this point, we've now addressed all parts of the question. As mentioned before, the X-bar chart is drawn above on the screen. And in addition, the process is in control as all points fall within the control limits without any unusual patterns. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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Key Concepts

X-bar Chart

Sampling

Control Limits

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