Question

Consider when businesses might use confidence intervals to estimate values, such as in sales projections, marketing results, and so forth. Describe a business decision that could be helped with confidence intervals. Be specific! Then create a problem with numbers from which another student could calculate a confidence interval and make a decision.

Answer 1

Solution :

Let me consider a specific business decision, where our organization, named – John Deere manufactures various heavy machinery equipment, such equipment needs various similar steel components which are required to weigh between a range, so these can be put into the cabin platform, as we are also taking such steel components from various vendors, thus, we need to get assure that how much we are confident that weight of various steel components will meet the ranges as defined or will meet the specifications as defined, let me consider if confidence Interval is 95%, then, we can conclude that we are 95% certain that mean weight of various steel components will meet the ranges as defined, further, confidence Interval can be considered as how the sample mean could be reliable and compared to the population mean,

Here, now let me create the actual problem, John Deere manufactures various heavy machinery equipments, such equipment needs various similar steel components which are required to weigh between a range, so called 140.50 and 149.25 grams, now we have taken random sample of around 50 steel components and we have evaluated the average weight of 144.45 grams, where standard deviation is 1.65 grams, here, formula for the Confidence Interval is = mean or average of sample data +/- [(Z value for a particular confidence Interval) * Standard Deviation]/Square Root of Number of samples,

Here, Confidence Interval = 144.45 +/-[1.96 for 95% confidence Interval * 1.65]/square root of 50,

Confidence Interval = 144.45 +/-[3.234/7.07]

= 144.45 +/- 0.46

= (143.99 to 144.91 )

From the above calculation, here, we have used 95% confidence level, based on that Z value is considered and here, we got Confidence Interval value 143.99 to 144.91 which fits within the specified range, here, specified range is 140.50 to 149.25 grams, we are 95% confident that mean weight of various steel components will meet the specification ranges as defined.

Let me know in the comment section if anything is not clear. I will reply ASAP!

If you like the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!