APU MATH530 Discussions Latest 2021 March (Full)

MATH530 Applied Statistics

Week 1 Discussion

You are to use this Discussion to introduce yourself and state your goals and objectives as they relate to our course. You are required to make a post to the Week 1 Introduction Discussion in order to complete your enrollment in the course. Your post must be at least 250 words, and you must complete it by the end of the first week. This is a university requirement. To make a post to the Week 1 Introduction Discussion, select the Introductions link, then select Start a New Conversation.  In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then select Post Message.

 Besides completing your enrollment in the course, the Week 1 Introduction Discussion is designed to 1) build peer-to-peer relationships by introducing oneself and one’s background to the class; 2) to articulate individual student learning goals and/or expectations for the class. Therefore, in your introduction you may wish to touch upon the following:

Who you are and how you would like to be addressed.

Your academic major or program of study.

Your current status in your program of study.

Your academic goals including why you are taking this course and what you hope to achieve by completing it.

Other information about yourself that you would like to share and might help others come to know you better.

MATH530 Applied Statistics

Week 2 Discussion

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

MATH530 Applied Statistics

Week 3 Discussion

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in "boom" state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1--and is.

State of economy            Probability          Market Return  Gold Return

Boom    0.15        25%        (-30%)

Moderate Growth           0.35        20%        (-9%)

Week Growth   0.25        5%          35%

No Growth         0.25        (-14%)   50%

Question #1: Compute the expected return for each alternative. Based on their expected returns, would you rather invest your money in the stock market or in gold? Why?

Next, compute the standard deviation of the return associated with an investment in gold and the standard deviation of the return associated with an investment in the market.

Question #2: Now, given their expected returns and the standard deviations of their returns, would you rather invest in gold or the stock market?  Why?

Questions 1 and 2 above can be answered using the material in Chapter 5 of our textbook. This last question goes well beyond those topics and is a real challenge. Suppose that in addition to investing in gold or in the stock market you could invest in a portfolio consisting of a combination of gold and the market. In particular, suppose that you could invest in a portfolio made up of 40% stock and 60% gold.

Question #3: Which of the 3 options would you prefer-(1) invest in gold alone, (2) invest in the market alone, or (3) invest 40% in the market and 60% in gold?  Why?

MATH530 Applied Statistics

Week 4 Discussion

Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!

Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?

MATH530 Applied Statistics

Week 5 Discussion

Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President's handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either "approve" or "strongly approve" of the President's handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who "approve" or "strongly approve" of the President's handling of the crisis in the financial markets.

Now, here's an interesting twist. If the same sample proportion was found in a sample twice as large-that is, 1150 out of 2560-how would this affect the confidence interval?

MATH530 Applied Statistics

Week 6 Discussion

A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds produced by the process is greater than 0.5 carat. To evaluate the profitability of the process, a sample of six diamonds was generated using this new process, with recorded weights .46, .61, .52, .48, .57, and .54 carat. Do the six measurements present sufficient evidence to indicate that the average weight of the diamonds produced by the new process is in excess of 0.5 carat? To answer this question conduct an appropriate test of hypothesis using the five step process outlined in our textbook and utilized in the solutions to the Chapter 8 review problems.

MATH530 Applied Statistics

Week 7 Discussion

During our course we have explored a number of different statistical applications and tools.  In this week's discussion you are to share how you intend to use one or more of the tools that we have examined in our course.  Be specific.  Be sure to include a description of the situation, the way in which you will employ the statistical tool you have selected, and provide some commentary about why you think the approach you have selected is appropriate and will prove to be useful.  This is your opportunity to consider--and then share--how you will employ the knowledge that you have gained during our course. I look forward to hearing from you.

Please keep in mind that my evaluation of your post will be based on the extent to which you participated and fostered a positive and effective learning environment--for yourself and others.  Participating and sharing are the keys.  Naturally, simply copying another person's post is prohibited.

MATH530 Applied Statistics

Week 8 Discussion

This discussion provides you an opportunity to share some final thoughts regarding our course. Please take the time to share your perspective with us.

Here are some questions that you may wish to consider as you prepare your post. You can reply to any of these questions, or make your own observations – whatever you think will be most helpful.

Which resources did you like best? Why?

Was the textbook adequate in explaining the concepts? If not, what was missing?

Was the material that we covered what you expected when you signed up for the course? What did you expect?

Will the information you learned be useful to you in the future, either in your future studies and/or on the job? Where will it be most useful do you think?

Would you prefer more/fewer assessments? Why?

Were the discussions useful to you in the course? Will they be useful to you in real life? Why?

Did you do better than (or worse than) you expected? Why?

What would you change about the course? What would you keep the same?

What degree are you working towards? Do you feel this course is helpful with regard to your chosen discipline?

What is your progress toward attaining your educational goals?

What course do you plan to take next? Why?

What advice can you share with others regarding your experience in our course or at APUS in general?