# Project #39530 - Statistics 3 One Sample Hypothesis Tests

Discussion initial question & Response

**The initial response should be at least 100 words. In addition, you should also reply to any questions classmates may have about your own post. The replies to classmates should be at least 50 words each and should be direct replies to classmates’ initial posts.

Discussion question #1.

Choose a single variable in your own organization or another organization in which you are interested.  Write a one-sample hypothesis test which would provide useful information to the organization.  Clearly indicate your null hypothesis, stating the value you expect for the variable.  Then describe the test you would use (are you using a directional or non-directional test; are you testing for a mean or for a proportion?).  Finally describe the sample you would need to take (what is the sample size; how would it be selected?).  Be sure to include the name of the variable you have chosen in the title of your post.

Focus on application in the replies to your classmates and indicate how your organization might use hypothesis tests similar to the ones your classmates are describing.

(((Red Lobster was recently sold or spun off by Darden Group due to) declining sales.  Darden will maintain ownership of Olive Garden, Longhorn Steakhouse, Capital Grille, Bahama Breeze and Season’s 52 restaurants.  For this hypothesis test I’d like to determine if the decline in sales at Red Lobster was also accompanied by a decline in sales per customer.  To do that, I’ll use a one-sample hypothesis test and compare per customer sales to statements made by the company that the average check was \$19.50 per customer (http://www.darden.com/pdf/about/red_lobster_ebrochure_2011.pdf).

The variable is the amount spent per customer.  That’s a quantitative (ratio) variable, so I’ll use a one sample hypothesis test for a mean.  The null hypothesis is that the mean (average) check is equal to or greater than \$19.50, or in a formula,

Ho: µ ≥ \$19.50

The alternative hypothesis, which I believe to be true, is that the average check is less than \$19.50, or in a formula:

Ha: µ < \$19.50

This is a lower tail test for a mean.  It is a lower tail test because I expect the value to be less than the hypothesized value.  It is a test for a mean because the amount of an individual check is a ratio variable; we’ll take a sample of checks from several individuals to calculate the average (or mean) check.

I want a margin of error (sampling error) of \$0.25 (25 cents) or less.  Using the Sample Sizes spreadsheet from Unit 2, and an estimated standard deviation of \$2.00, I need a sample of 246 meals.  Rounding up a little, I would collect a random sample of 250 sales receipts from all stores over from the last quarter of 2013.  That’s not to say I would get data from all 700 restaurants (http://www.redlobster.com/press/fact_sheet/).  Instead, 250 receipts would be selected randomly from all meals served at all 700 restaurants over that three month period.  With that random selection process, the sampling error should be accurately predicted by the Sample Sizes spreadsheet.  If sales have decreased by 25 cents or more, that will be outside my margin of error and the null hypothesis will be rejected.))))))))))))))))))))))))))))))))

Classmate Response#1A:(50 words minimum) Will present classmate response tomorrow once they upload their answer

Classmate Response#1B:(50 words minimum) Will present classmate response tomorrow once they upload their answer

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Assignment

Use the Student_Data.xls file which consists of 200 MBA students at Whatsamattu U. The file includes variables regarding students’ age, gender, major, GPA, Bachelors GPA, course load, English speaking status, family, weekly hours spent studying. Each of the three assigned problems should be formatted as a one page memo. Answers to all three of the problems should be submitted via the Drop Box as a single Word document with each of the problems clearly labeled. Be sure to include your name on the document itself!

COMPLETE PROBLEM 1: It is pretty common across most schools to find the grades at the MBA level divided between A’s and B’s. As such, you expect the mean GPA to be around 3.50. Using the sample of 200 MBA students, conduct a one-sample hypothesis test to determine if the mean graduate GPA is different from 3.50. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart (a bar chart or column chart will probably work best) comparing the calculated mean with the hypothesized mean.

COMPLETE PROBLEM 2: Assume you read in the Whatsamatta U website that the average age of their MBA students is 45. Is this really true or have they failed to update this correctly? You think it is far less because more students have started their Masters sooner since the economy is so bad. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the mean age is less than 45. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart (a bar chart or column chart will probably work best) comparing the calculated mean with the hypothesized mean.

COMPLETE PROBLEM 3: You have heard from idle chatter that most students don’t declare a major in their MBA programs. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the proportion without a major is greater than 50%. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart (a bar chart or column chart will probably work best) comparing the calculated proportion with the hypothesized proportion.

 Subject Mathematics Due By (Pacific Time) 09/09/2014 04:30 pm
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