You are to use this Discussion to introduce yourself and state your goals and objectives as they relate to our course.
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?
MATH530 Applied Statistics
Quiz 1
Question 1 Identify whether the variable in the information below is qualitative or quantitative. Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environment Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample.
Question options:
quantitative
qualitative
qualitative as well as quantitative
neither qualitative nor quantitative
Information does not have any variable
Question 2 Wetlands offer a diversity of benefits. They provide habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years the United States has lost more than half its wetlands. Suppose Environmental Almanac gives the percentage of wet lands lost in each state in the last 200 years as noted in the table below.
The distribution of the percentage loss of wetlands per state is approximately mound shaped.
Question options:
false
true
Question 3 In a biology class, the final grade is based on several things: a lab score, score on two major tests, and the score on the final exam. There are 100 points available for each score. However, the lab score is worth 30% of your total grade, each major test is worth 22.5%, and the final exam is worth 25%. Compute the weighted average for the following scores: 90 on the lab, 82 on the first major test, 91 on the second major test, and 84 on the final exam. Round your answer to the nearest hundredth.
Question options:
88.42
85.12
86.62
86.92
84.90
Question 4 Finish times (to the nearest hour) for 59 dogsled teams are provided. Draw a relative frequency histogram. Use five classes.
261 270 236 244 278 296 284 297 287 287 250 256
338 360 341 333 261 267 287 296 313 311 309 309
299 303 277 283 304 305 286 290 286 287 297 299
332 330 309 329 309 329 285 291 295 298 306 315
310 318 318 320 333 321 323 324 327 302 319
Question options:
Question 5 Given the sample data, 13, 32, 28, 13, 12, 23, compute the sample standard deviation.
Question options:
8.71
24.20
63.14
75.77
7.95
MATH530 Applied Statistics
Quiz 2
Question 1 Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches, what percentage of women are taller than 67.5 inches?
Question options:
0.1%
15.9%
97.7%
50.0%
84.1%
Question 2 Find the area under the standard normal curve between z = -1.9 and z = 1.8.
Question options:
0.036
0.471
0.029
0.964
0.935
Question 3 Let z be a random variable with a standard normal distribution. Find P(-2.9 < z < 0.4).
Question options:
0.994
0.654
0.002
0.498
0.155
Question 4 Assume that X has a normal distribution, with mean, , and standard deviation, . Find P(7 < X < 18).
Question options:
0.999
0.369
0.001
0.630
1.000
Question 5 A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 56 months and a standard deviation of 6 months. If the company does not want to make refunds for more than 10% of its batteries under a full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Question options:
56 months
67 months
48 months
44 months
63 months
MATH530 Applied Statistics
Quiz 3
Question 1 Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.7 seconds. Suppose that you want to set up a statistical test to challenge the claim of 6.7 seconds. What would you use for the null hypothesis?
Question options:
f$mu > 6.7 secondsf$
f$mu = 6.7 secondsf$
f$mu < 6.7 secondsf$
f$mu neq 6.7 secondsf$
Question 2 Let X be a random variable representing the dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation f$sigma =f$ 2.8%. Now, suppose we wish to test the null hypothesis that f$mu =f$ 6.4% against the alternative that f$mu >f$ 6.4% using a level of significance of f$alpha =f$ .05. To do so, a random sample of 16 Australian bank stocks is observed and has a sample mean of f$bar{x} =f$ 8.91%.What is the value of the test statistic?
Question options:
-0.224
-3.586
3.586
0.896
Question 3 Let X be a random variable representing the dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation f$sigma =f$ 2.8%. Now, suppose we wish to test the null hypothesis that f$mu =f$ 6.4% against the alternative that f$mu >f$ 6.4% using a level of significance of f$alpha =f$ .05. To do so, a random sample of 16 Australian bank stocks is observed and has a sample mean of f$bar{x} = f$ 8.91%. What is the p-value associated with this test?
Question options:
.0002
.0500
.0100
.0068
Question 4 Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation f$sigma = 2.4f$ % . A random sample of 19 Australian bank stocks has a sample mean of f$bar{x} f$ = 8.71%. For the entire Australian stock market, the mean dividend yield is f$mu f$ = 5.9%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9%? Use f$alpha f$ = .05. Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis?
Question options:
The p-value is less than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.
The p-value is less than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.
The p-value is greater than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.
The p-value is greater than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.
The p-value is less than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.
Question 5 Benford’s Law claims that numbers chosen from very large data files tend to have “1” as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with “1” as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 397 numerical entries from the file and r = 110 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using f$alpha =f$ 0.1. What is the value of the test statistic?
Question options:
20.704
0.052
-20.704
-0.052
-1.039
MATH530 Applied Statistics
Exam 1
125
157
113
127
201
165
145
119
148
158
148
168
117
105
136
136
125
148
108
178
179
191
225
204
104
205
197
119
209
157
209
205
221
178
247
235
217
222
224
187
265
148
165
228
239
245
152
148
115
150
Question 1 The following data are the base salaries, in thousands of dollars, of a sample of 50 chief executive officers of companies doing business with the state of Connecticut.
Find the mean of the CEO salaries, rounded to the nearest thousand dollars.
Question 2 The following data are the base salaries, in thousands of dollars, of a sample of 50 chief executive officers of companies doing business with the state of Connecticut.
125
157
113
127
201
165
145
119
148
158
148
168
117
105
136
136
125
148
108
178
179
191
225
204
104
205
197
119
209
157
209
205
221
178
247
235
217
222
224
187
265
148
165
228
239
245
152
148
115
150
Find the median of the CEO salaries, rounded to the nearest thousand dollars.
Question 3 The following data are the base salaries, in thousands of dollars, of a sample of 50 chief executive officers of companies doing business with the state of Connecticut.
125
157
113
127
201
165
145
119
148
158
148
168
117
105
136
136
125
148
108
178
179
191
225
204
104
205
197
119
209
157
209
205
221
178
247
235
217
222
224
187
265
148
165
228
239
245
152
148
115
150
Find the variance of the CEO salaries, rounded to the nearest ten. (Don’t worry about the units.)
Question 4 The following data are the base salaries, in thousands of dollars, of a sample of 50 chief executive officers of companies doing business with the state of Connecticut.
125
157
113
127
201
165
145
119
148
158
148
168
117
105
136
136
125
148
108
178
179
191
225
204
104
205
197
119
209
157
209
205
221
178
247
235
217
222
224
187
265
148
165
228
239
245
152
148
115
150
Find the standard deviation of the CEO salaries, rounded to the nearest thousand dollars.
Question 5 The following data are the base salaries, in thousands of dollars, of a sample of 50 chief executive officers of companies doing business with the state of Connecticut.
125
157
113
127
201
165
145
119
148
158
148
168
117
105
136
136
125
148
108
178
179
191
225
204
104
205
197
119
209
157
209
205
221
178
247
235
217
222
224
187
265
148
165
228
239
245
152
148
115
150
.
Find the interquartile range of the CEO salaries, rounded to the nearest thousand dollars.
MATH530 Applied Statistics
Exam 2
Question 1 It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average? Place your answer, rounded to the nearest whole number, in the blank.______
Question 2 The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and standard deviation 2.2 minutes. For a door selected at random, what is the probability the assembly line time will be between 5 and 10 minutes? Place your answer, rounded to 4 decimal places, in the blank.______
Question 3 The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.______
Question 4 Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. Suppose that one such poll asks voters how they feel about the President’s handling of foreign affairs. The results show that 575 out of the 1280 people polled say they either “approve” or “strongly approve” of the President’s handling of foreign affairs. Based on the results of this sample, 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 foreign affairs. Place your answer, rounded to 4 decimal places, in the blanks. Lower limit =___; and upper limit =______
Question 5 Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. Suppose that one such poll asks voters how they feel about the President’s handling of foreign affairs. How large a sample must the pollster take to ensure that, with 95% confidence, he or she could estimate the fraction of voters who “approve” or “strongly approve” of the President’s handling of foreign affairs within 2% of the actual value? Place your answer, rounded to the nearest whole number, in the blank.______
MATH530 Applied Statistics
Exam 3
Question 1 Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Use these data to answer questions 1 through 5.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
If we wish to determine if the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, the null hypothesis would be
Question options:
Ho:
Ho:
Ho:
Ho:
Question 2 Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Use these data to answer questions 1 through 5.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
If we are interested in determining if the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, the alternative hypothesis would be
Question options:
H1: f[mu _{d}=0f]
H1: f[mu _{d}>0f]
H1:
H1:
Question 3 Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Use these data to answer questions 1 through 5.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?
Question options:
z = 1.8424
t = 1.8424
t = 2.7234
p = 2.7234
Question 4 Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Use these data to answer questions 1 through 5.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
What is the p-value associated with the test of hypothesis you conducted?
Question options:
p = .057403
p = .114986
p = .942597
p = .885014
Question 5 Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Use these data to answer questions 1 through 5.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
At the .05 level of significance, is there sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?
Question options:
no
yes
It is impossible to determine
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