Question

Confidence Intervals

Do the calculations on paper. Show all work by writing the equation in symbol format first. Then define each symbol in terms of the problem. Show each step of your calculation, skipping no step (each division, each addition, each multiplication.) When you have your final answer(s), draw a box around them. Copy and paste the image(s) into your document and label the image(s.) [That is to say, some people write larger, some smaller, some may get the work to fit nicely on half a page, others may take two and a half pages... Grade not based on how many pages... Grade based on reasonable work which can be read and followed. If you type it out, great. But if you do not, also great. Still show all work, no skipped steps.] Use software to replicate your answers. Paste in output to verify software use. [Excel, Minitab, StatCrunch, other apps...as your choice, just reference what you used...if on a page, give hyperlink to page, but do make sure you paste in work.]

Then explain your answer in words. Make a confidence statement. Explain its limitations, and its risks. [how sure are you that you are right; what are the costs and probability that you are wrong.

A1 Eddie is the manager of a small grocery store in Alabama, which is part of a large chain, but serves a rural community. His store had begun offering online ordering, with store parking lot pickup last year. It was not a big thing, as so many people socialized when they "came to town to shop. This last month, things have changed. More of his regular customers are doing online shopping/parking lot pickup. He did a random sample from the last two weeks, choosing a sample of 49 from the 589 orders. The mean of his sample was $85.00, with a standard deviation of $15.00.  Choose a confidence interval [80, 90, 95, or 99] and explain why that percent would work for this question.   Create a confidence interval of the mean to predict the average dollar of sales. Make a statement, using the results from your calculations, rounding reasonably.

Answer 1

Eddie is running a grocery store and he wants an estimate about the average dollar sales online.

Now he is doing this to plan his inventory. Hence have a good estimate rather than an exact estimate is important. Hence the ideal level of the confidence interval is 95%.

80% confidence interval may be too small and he may miss out the true population mean.

On the other hand, 99% confidence interval will be too large and be not recommended for such planning.

Hence find the confidence using 95% confidence interval.( Note: This an R output, which is format to give easy to understand results.)

We are 95% confident that the true population mean sales lies between 80.6915 to 89.3085.

In other words we can also say if Eddie repeatedly takes multiple samples of size 49 from the population of 589, 95% of times the mean average will fall in this interval.