Your work should be done in Excel. Do each problem on its own Excel tab(s), and label the Excel tabs by problem number. If you want to use more than one Excel tab to address a problem then label the tabs “3 a” “3 b” or “2” “2 cont’d” etc. Provide the detail (FORMULAS!) of your calculations in Excel, step-by-step, whenever possible. Don’t just type in numbers if you’ve acquired them by doing a calculation somewhere! If you are using automatic Excel output, do feel free to display it directly (there would be no formulas within it). If you’re asked to comment or provide conclusions, then merge Excel cells and wrap text so that you can write your responses neatly into cells. Feel free to copy/paste the data from my starting (or ‘raw’) Excel files in Canvas, into your own Excel tab(s) to begin each problem. Make sure that you address the specific questions asked of you and that you make your responses easy to find and read. Organize your work. Take care to write carefully (with good spelling, grammar, and punctuation) if you’re explaining something (even though it’s just in Excel cells!). Make your answers easy to follow! As you have weeks to do this assignment it is a reasonable use of your time to “polish” the presentation of your submission
1. Refer to the Excel “TeleMed” data posted on eLearning which considers the savings amounts of a sample of patients who used the online TeleMed services rather than conducting a typical office visit. (15)
a. Assume we know nothing about the underlying population distribution of all patients who use TeleMed. If you may legitimately do so, then create a 95% confidence interval for the mean amount of money saved by a TeleMed patient based on your sample. If you may not legitimately construct such a confidence interval, explain why you may not do so in a sentence or two.
b. Assume we know the underlying population distribution of all patients who use TeleMed is normal. If you may legitimately do so, then create a 99% confidence interval for the mean amount of money saved by a TeleMed patient based on your sample. If you may not legitimately construct such a confidence interval, explain why you may not do so in a sentence or two.
c. We’re curious whether the real, population proportion of TeleMed patients who have highspeed internet at home is actually 60%. If you may legitimately do so, then create a 90% confidence interval for the proportion of TeleMed patients that have highspeed internet at home based on your sample. If you have a legitimate interval, comment on your impression of whether the real population proportion of TeleMed patients with highspeed internet access at home is actually 60%. If you may not legitimately construct such a confidence interval, explain why you may not do so in a sentence or two.
2. Refer to the Excel “Tub Sales” data posted on eLearning which considers the sales performance last year of a sample of the Rub-a-Dub company’s sales force: (40)
Do NOT use the “finite population” corrections for standard deviation calculation in this problem. Just assume we’re dealing with an infinite population.
a. Provide the formal null and alternative hypotheses for a hypothesis test of the question of whether or not the mean tub sales is really $92,000.
Assume that the underlying population of tub sales is normally distributed.
b. Conduct this hypothesis test based on the 90% confidence level (*Note, my original version here said 90% ‘significance’ level, but that’s a sloppy description on my part…I do indeed mean the standard case where a = 0.10). What is the p-value? Do you reject or fail to reject your null hypothesis from (a)? Why?
c. Create a 95% confidence interval for the mean tub sales. Explain in a sentence, in layman’s terms, what this confidence interval implies. Would your interval suggest rejecting or failing to reject your null hypothesis from (a) based on this interval (at the 95% level)? Why?
d. Compare your conclusions (about rejecting the null hypothesis, or not) in part “b” to part “c”. Do these results conflict with each other? (i.e., is it OK to find these two answers simultaneously?...if so, why?...OR, is there a conflict where it should be impossible for these results to occur simultaneously?)
e. If I ignored my earlier assumption and told you that the underlying population of tub sales was NOT normally distributed, how would this change your responses to parts “b” and “c”?
f. If I ignored my earlier assumption and told you that the underlying population of tub sales was NOT normally distributed, BUT, your final calculations (p-value for “b”, confidence interval for “c”) were based on double the sample size (a sample of 40 salesmen, rather than 20), would this change your response to part “e”? If so, why? If not, why not?
You may ignore the above questions and return to the raw “Tub Sales” data.
g. The company boasts that at least 70% of its salesmen have college degrees. Provide the formal null and alternative hypotheses for a test of this question. Is this a one or two-tailed hypothesis?
h. Do you have a large enough sample to conduct the correct hypothesis test? Explain with a calculation why or why not. (Hint: you need to use a specific rule taken directly from our course slides that fits this scenario’s sampling distribution)
i. If your answer to part “h” is yes, then conduct this hypothesis test based on the 95% confidence level. Do you reject or fail to reject your null hypothesis? Why?
3. Refer to the Excel “Avionics” data posted on eLearning. This data shows sales amounts, by order, of the Avionics Group which sells a wide variety of cables and adapters for electronic aviation equipment. The population of Avionics’ sales data is normally distributed. Last year, the mean value of orders placed with the Avionics Group was $47.27, and management wants to assess whether the mean value of orders placed to date this year is the same as last year. (15)
a. Formulate hypotheses that can be used to test whether the mean value of orders placed this year differs from the mean value of orders placed last year.
b. Use the data to conduct your hypothesis test. What is the p-value for your hypothesis test? At a = 0.01 what is your statistical conclusion?
c. You want to report your findings to management. In a sentence or two, how would you describe your statistical and practical findings?
4. It would be relatively easy and inexpensive to implement the new machinery, and management is very eager to take on the minimal new expenses if they believe the new machinery will increase units by more than 100/day. (15)
a. As the consultant, which of the three following null/alternative hypothesis pairs do you propose to test? (circle one of the three Ho:/Ha: choices below)
Ho: m < 100 more units/day Ho: m = 100 more units/day Ho: m > 100 more units/day Ha: m > 100 more units/day Ha: m equal 100 more units/day Ha: m < 100 more units/day
Why did you choose the test you chose? (answer in a sentence or two)
b. Given your above selection, what would be the consequence of making a “Type I Error”? What would be the consequence of making a “Type II Error”? Do not just recite the textbook definitions of Type I and II error…describe what the practical meanings of Type I and II error are IN THIS SCENARIO! Which of these is a more harmful error to make in this case? Explain why in a sentence or two.
c. Given your answer to part “b” (in particular the “more harmful error” question) would you prefer to utilize a 90% or 99% confidence level hypothesis test? Explain why in a sentence or two.
In Excel, create a tab and label it “4. New Machinery” (because this is question 4) and write your answers there to these questions.
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