STAT 200: Introduction to Statistics Final Examination, Spring 2016 OL4 Page 1 of 7 STAT 200 OL4/US2 Sections Final Exam Spring 2016 The final exam will be posted at 12:01 am on May 6, and it is due at 11:59 pm on May 8, 2016. Eastern Time is our reference time. This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. Answer all 20 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from calculators, programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or hand-held calculators to aid in your calculation, you must cite the sources and explain how you get the results. Record your answers and work on the separate answer sheet provided. This exam has 200 total points; 10 points for each question. You must include the Honor Pledge on the title page of your submitted final exam. Exams submitted without the Honor Pledge will not be accepted. STAT 200: Introduction to Statistics 1. Final Examination, Spring 2016 OL4 Page 2 of 7 True or False. Justify for full credit. (a) (b) (c) (d) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.2. If all the observations in a data set are identical, then the variance for this data set is 0. The mean is always equal to the median for a normal distribution. It's easier to reject the null hypothesis at significance level of 0.01 than at significance level of 0.05. (e) In a two-tailed test, the value of the test statistic is 2. If we know the test statistic follows a Student's t-distribution with P(T >2) = 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance. 2. Identify which of these types of sampling is used: cluster, convenience, simple random, systematic, or stratified. Justify for full credit. (a) The quality control department of a semiconductor manufacturing company tests every 100th product from the assembly line. UMUC STAT Club wanted to estimate the study hours of STAT 200 students. Two STAT 200 sections were randomly selected and all students from these two sections were asked to fill out the questionnaire. A STAT 200 student is interested in the number of credit cards owned by college students. She surveyed all of her classmates to collect sample data. In a career readiness research, 100 students were randomly selected from the psychology program, 150 students were randomly selected from the communications program, and 120 students were randomly selected from cyber security program. (b) (c) (d) 3. The frequency distribution below shows the distribution for commute time (in minutes) for a sample of 50 STAT 200 students on a Friday afternoon. (Show all work. Just the answer, without supporting work, will receive no credit.) Commute Time (in minutes) Frequency Relative Frequency 1 - 14.9 5 15 - 29.9 10 0.20 30 - 44.9 45 - 59.9 20 60 or above Total (a) (b) 50 Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places. What percentage of the commute times was at least 30 minutes? STAT 200: Introduction to Statistics Final Examination, Spring 2016 OL4 Page 3 of 7 (c) Does this distribution have positive skew or negative skew? Why? 4. The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of 500 students. Quiz 1 Quiz 2 Minimum Q1 Median Q3 Maximum 15 20 35 35 55 50 85 90 100 100 For each question, give your answer as one of the following: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes have the same value requested; (iv) It is impossible to tell using only the given information. Then explain your answer in each case. (a) (b) (c) Which quiz has less range in grade distribution? Which quiz has the greater percentage of students with grades 85 and over? Which quiz has a greater percentage of students with grades less than 60? 5. A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box, then replacing it in the box and drawing a second marble from the box. (Show all work. Just the answer, without supporting work, will receive no credit.) (a) (b) List all outcomes in the sample space. What is the probability that neither marble is red? fraction form) 6. There are 1000 students in a high school. Among the 1000 students, 250 students take AP Statistics, and 300 students take AP French. 100 students take both AP courses. Let S be the event that a randomly selected student takes AP Statistics, and F be the event that a randomly selected student takes AP French. Show all work. Just the answer, without supporting work, will receive no credit. (a) (b) Provide a written description of the complement event of (S OR F). What is the probability of complement event of (S OR F)? 7. Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be the event that the first one lands on 6. (a) What is the probability that the first one lands on 6 given that the sum of the two dice is 8? Show all work. Just the answer, without supporting work, will receive no credit. Are event A and event B independent? Explain. (b) (Express the answer in simplest STAT 200: Introduction to Statistics 8. (a) (b) 9. Final Examination, Spring 2016 OL4 Page 4 of 7 There are 8 books in the \"Statistics is Fun\" series. (Show all work. Just the answer, without supporting work, will receive no credit). How many different ways can Mimi arrange the 8 books in her book shelf? Mimi plans on bringing two of the eight books with her in a road trip. How many different ways can the two books be selected? Assume random variable x follows a probability distribution shown in the table below. Determine the mean and standard deviation of x. Show all work. Just the answer, without supporting work, will receive no credit. x P(x) -2 0.1 0 0.2 1 0.3 3 0.1 5 0.3 10. Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.40. (a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (b) Find the probability that she gets at least 2 cherry tomato seedlings. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit. 11. Assume the weights of men are normally distributed with a mean of 172 lbs and a standard deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no credit. (a) (b) Find the 90th percentile for the distribution of men's weights. What is the probability that a randomly selected man weighs more than 185 lbs? 12. Assume the IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. Show all work. Just the answer, without supporting work, will receive no credit. (a) (b) If a random sample of 25 adults is selected, what is the standard deviation of the sample mean? What is the probability that 25 randomly selected adults will have a mean IQ score that is between 95 and 105? 13. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 95% confidence interval estimate of the proportion of adults believing in global warming. Show all work. Just the answer, without supporting work, will receive no credit. STAT 200: Introduction to Statistics Final Examination, Spring 2016 OL4 Page 5 of 7 14. In a study designed to test the effectiveness of acupuncture for treating migraine, 100 patients were randomly selected and treated with acupuncture. After one-month treatment, the number of migraine attacks for the group had a mean of 2 and standard deviation of 1.5. Construct a 95% confidence interval estimate of the mean number of migraine attacks for people treated with acupuncture. Show all work. Just the answer, without supporting work, will receive no credit. 15. Mimi is interested in testing the claim that more than 75% of the adults believe in global warming. She conducted a survey on a random sample of 100 adults. The survey showed that 80 adults in the sample believe in global warming. Assume Mimi wants to use a 0.05 significance level to test the claim. (a) (b) (c) (d) 16. Identify the null hypothesis and the alternative hypothesis. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that more than 75% of the adults believe in global warming? Explain. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table. Subject 1 2 3 4 5 Number of Words Recalled 1 hour later 24 hours later 14 12 18 15 11 9 13 12 12 12 Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Assume we want to use a 0.10 significance level to test the claim. (a) (b) (c) Identify the null hypothesis and the alternative hypothesis. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. STAT 200: Introduction to Statistics Final Examination, Spring 2016 OL4 Page 6 of 7 (d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion. 17. (a) (b) (c) (d) 18. In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats per minutes. Use a 0.05 significance level to test the researcher's claim.. Identify the null hypothesis and alternative hypothesis. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the researcher's claim? Explain. The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 500 purchases yields observed counts 150, 120, 110, and 120 for types 1, 2, 3, and 4, respectively. Type Number 1 150 2 120 3 110 4 120 Assume we want to use a 0.05 significance level to test the claim that the four types are equally popular. (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit. (d) Is there sufficient evidence to support the manager's claim that the four types are equally popular? Justify your answer. 19. A random sample of 4 professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars). x y (a) (b) 0 1 1 2 2 4 5 8 Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. Based on the equation from part (a), what is the predicted value of y if x = 3? Show all work and justify your answer. STAT 200: Introduction to Statistics Final Examination, Spring 2016 OL4 Page 7 of 7 20. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. Mimi wants to test the claim that the mean weight loss is the same for the 10 programs. (a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square (Show all work): Source of Variation Factor (Between) Error (Within) Total (b) (c) (d) Sum of Squares (SS) Degrees of Freedom (df) Mean Square (MS) 42.36 1100.76 N/A Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that the mean weight loss is the same for the 10 programs at the significance level of 0.05? Explain. Thanks working on it. TABLE OF CONTENTS 1. EXECUTIVE SUMMARY.......................................................................................................... 2 2. DESCRIPTION OF PRODUCTS AND SERVICES.......................................................................... 2 3. TECHNOLOGY CONSIDERATIONS........................................................................................... 2 4. PRODUCT/SERVICE MARKETPLACE....................................................................................... 3 5. MARKETING STRATEGY........................................................................................................ 4 6. ORGANIZATION AND STAFFING............................................................................................. 4 7. SCHEDULE............................................................................................................................. 5 8. FINANCIAL PROJECTIONS ...................................................................................................... 5 9. FINDINGS AND RECOMMENDATIONS ..................................................................................... 6 1. EXECUTIVE SUMMARY BC is leading in the amount of sales of chocolates all over the United States. Their products are delivered from the 50 warehouses and they are well known for their disputable good quality and good services to their clients. However as much as for the last 10 years the sales of this firm have been increasing, the rate has been affected and it has slowed in a substantial amount. One important factor that has led to this decline, is change in the market place. People are now buying chocolate from online market and this has drastically affected the BC s sales. Albeit the firm has maintained an active website, it is not able to host a platform for e- commerce so that it could conduct online sales. Therefore this shows how the firm is losing sales to competitors who have been able to take their market online. The chocolate and confections marketplace is healthy and shows a continued growth trajectory over the next five to ten years. However the firm has an high potential to open up their market online to extend the already existing market by making use of thre existing technology, and conducting best industrial practices advertising and becoming more active in marketing, and this will finally see the firm experience its projected growth in future. 2. DESCRIPTION OF PRODUCTS AND SERVICES BC is looking into how it can create an online platform where it can sell its products. Up to now the firm has been limited to selling their products through the mortar and brick chain from their stores and this has limited their sales to geographical areas around their stores. Due to this the firm has been unable to cope with the high trend of the growing online market.by offering an online platform for selling the product the firm will be opening a purely new market which will lead increase of their sales p, profit and sequentially their growth. Customers will always find a it easy to buy from their most convenient places and the online platform will be a great market place for them. The pupose of this document is not to change the line of products the firm is offering to the market but to provide a more convenient market for their potential customers as well as expanding the market. Therefore any change to the product offered by the firm is not as a result of the report by this paper. 3. TECHNOLOGY CONSIDERATIONS This section should explain any considerations the organization must make with regards to technology. Many new initiatives rely on technology to manage or monitor various business functions. New technology may be developed internally or contracted through a service provider and always result in costs which must be weighed in determining the path forward. Feasibility Study Template www.ProjectManagementDocs.com 3 Upgraded technological capability will be required for ABC to move toward offering an online marketplace from which customers may purchase our products. Customers demand a simple and easy way by which to conduct online transactions and it is imperative that all transactions are conducted in a secure manner. While ABC maintains a web site with product lists and descriptions, it does not currently allow for purchasing to be done online. This functionality must be integrated with our current web site to allow for secure purchases to be made. Additionally, new online marketing functionality must be considered in order to target existing and potential customers through methods such as e-mailing lists, promotional advertisements, and loyalty discounts. While ABC maintains a small information technology (IT) group, the expertise does not currently exist internally to design, build, and implement the sort of extensive online platform required for this effort. Therefore, the recommendation is to contract this work out to an internet marketplace provider who can work with ABC to meet its needs within the determined timeframe and budget. It should be noted that while ABC does not have this expertise internally, the technology exists and is in use throughout the marketplace which lowers the risk of this concept considerably. ABC currently maintains a high speed internet connection, web server, and the latest software. With the addition of an e-commerce portal it is expected that there will be an overall cost increase of 510% for web server operations and maintenance costs. 4. PRODUCT/SERVICE MARKETPLACE This section describes the existing marketplace for the products and/or services the organization is considering. It may describe who the target market consists of for these products or services, who the competitors are, how products will be distributed, and why customers might choose to buy our products/services. Most marketplaces are dynamic environments in which things change constantly. To enter a new marketplace blindly will usually result in an organization not fully understanding its role and not maximizing its resulting benefits. The online marketplace for chocolates and confections has been thriving for many years. In FY20xx online chocolate sales accounted for approximately $20 million or 20% of total chocolate sales worldwide. While chocolates and confections are available in almost every store, our primary marketplace consists of specialty chocolates and confections. All of ABC's current major competitors already have an established online presence of at least 3-5 years. The top 3 competitors are currently: Smith's Chocolates, Worldwide Candy, and Chocolate International. A large majority of ABC's customer base are returning customers and referrals from existing customers. By providing a more convenient means of purchasing our products online it is expected that we will retain these customers while conducting an online marketing campaign for new customers as well. ABC will distribute online purchases via direct shipping from the nearest store location. This will allow ABC to provide timely shipping and eliminate the need for a central warehouse or Feasibility Study Template www.ProjectManagementDocs.com 4 Facility from which to store and ship its products. Such a facility would require a significant capital investment as well as increased operation and maintenance costs. However, based on anticipated growth projections, ABC must ensure that all store locations maintain adequate inventories on hand to satisfy customer demand. 5. MARKETING STRATEGY This section provides a high level description of how the organization will market its product or service. Some topics which should be included are: how does an organization differentiate itself from its competitors; types of marketing the organization will utilize; and who the organization will target. Marketing efforts must be focused on the right target groups in order to yield the greatest return on investment. In order to be successful, ABC must differentiate itself from competitors in order to appeal to customers in the online marketplace. To do this, ABC will utilize its practice of personalizing its product packaging which it currently offers in-store customers. Current competitors do not currently provide any personalization of packaging. Customers will have the ability to personalize messages on or inside of product packaging, request specific color-based themes, or tailor packaging for special occasions or events. ABC will implement a customer e mailing list in order to send product promotions, sales advertisements, and other special offerings to customers who register. Additionally, ABC will offer referral incentives to customers who refer our products to friends and family in order to provide additional incentives. ABC will also maintain a customer database in order to determine its target customer groups and geographical regions. ABC will research marketing intelligence providers to determine the benefits and costs of purchasing customer information for bulk email campaigns as well. Another important consideration of ABC's online marketing strategy is cost. Electronic marketing communication costs are very small in comparison to direct mail marketing which ABC currently utilizes. However, we expect the additional revenue from online sales to greatly outweigh these additional electronic marketing costs. It is important to note that ABC's current marketing and sales staff will require training in online marketing and sales practices. This training will need to be contracted to a training provider as part of our startup costs and schedule. 6. ORGANIZATION AND STAFFING Any change in an organization either by change of product or change of operation structure, there is always need for restricting the organization by either changing the staff, increasing staff, of even reducing the staff in order to for the change to fit in the system. It is always important to put this into consideration as this may result to increased cost or require the firm to entirely change its operating process as well as its structure. However the firms' campaign for online sales is not meant to substantially affect the structure of the organization. , though there is need for increased number of staff in order to implement the campaign successfully. The departments should work within the existing structure that is reporting to the department managers. Position 1: Online Sales Manager -this will be a full time position which will lead the sales staff in identifying opportunities for sales and finding a way out to change the opportunities to real sales. The sales manager will work from the headquarters and reporting to the marketing director. Position 2: Online Marketing Manager - this will also be a full time position leading the marketing staff in finding the targeted markets, that is potential customer and groups and carrying out advertisement online and ensure there is always maximum traffic online. The person will too work from the headquarters and reporting to the marketing director. 7. SCHEDULE. The XY campaign on online sales, is anticipated to take up to six months after the project approval to the time of launching the e- commerce platform. This is because most of the foundations for the platform are readily available. The schedule for some of the big milestones for the platform are as follows. March 2, 10xx: Initiate Project April 3, 10 xx: meeting for project kick off May 4, 10 xx: Complete the design for online sales June 2, 10 xx: Complete a testing for the site. July 3, 10 xx: Complete a beta testing of the sales site. August 4, 10 xx: launch the online sale site live. On approval of the project a detailed schedule will be availed by the team tasked the project and it will include the tasks and all deliverables. 8. FINANCIAL PROJECTIONS There is always expected or projected change in financial management with change in the system. Financial projections for the added online sales platform for XY are summarized in the table below. The figures in the table account for expected online sales, added staff, material, insurance and shipping. Support for IT and the training required cost for hosting and the web server are also part of the cost and insurance costs, contract support for IT and training needs, and web server and hosting costs. Assumptions for the projections are: In store sales projections remain unchanged All milestones are performed in accordance with the schedule All transactions are closed yearly with no carry-over to subsequent years 9. FINDINGS AND RECOMMENDATIONS According to information provided in this feasibility study, the firm XY recommended to accept or approve the initiative for online sales and initiate the project. Findings of the study shows that the project will be high benefit to the firm and it is likely to succeed. The main findings were as follows. Technology: The project will use the existing technology and hence lowering the risk. The infrastructure will be contracted to a vendor and hence sharing the risk The technology is simple to maintain and operate at a low cost. Marketing: Initiative will give the firm room to reach high number of targeted group's e at a affordable cost XY can expand market base beyond regional areas close to the stores. The online sales market is growing steadily. Organizational: additional staff should be minimal with no change to structure of the organization No new capital require to be invested or addition of new facilities Financial: Break even point will be early, especially the second year in operation The projection for the five years indicate that online sales account for 25% of the total sales. By maintaining both the in-store and online sales the firm will be able to capture more market share. REFFERENCES STAT 200 Introduction to Statistics Name______________________________ Final Examination: Spring 2016 OL4/US2 Instructor __________________________ Answer Sheet Instructions: This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. Record your answers and work in this document. Answer all 20 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from calculators, programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or hand-held calculators to aid in your calculation, please cite the source and explain how you get the results. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. Your exam will receive a zero grade unless you complete the following honor statement. Record your answers and work. Problem Number 1 Answer: Solution (a) (b) (c) (d) (e) Justification: Answer: (a) (b) (c) (d) 2 Justification: 3 Answer: (a) Commute Time (in minutes) Frequency Relative Frequency 1 - 14.9 5 15 - 29.9 10 30 - 44.9 45 - 59.9 60 or above Total (b) (c) Work for (a) and (b): Answer: (a) (b) 4 (c) Justification : Answer: (a) (b) 5 Work for (b): 0.20 20 50 Answer: (a) (b) 6 Work for (b): Answer: (a) (b) 7 Work for (a) and (b): Answer: (a) (b) 8 Work for (a) and (b): Answer: Work: 9 Answer: (a) (b) 10 Work for (b) : Answer: (a) (b) Work for (a) and (b): 11 Answer: (a) (b) 12 Work for (a) and (b): 13 Answer: Work: Answer: Work: 14 Answer: (a) (b) (c) (d) 15 Work for (b) and (c): 16 Answer: (a) . (b) (c) (d) Work for (b) and (c): Answers: (a) (b) (c) (d). 17 Work for (b) and (c): 18 Answer: (a) (b) (c) (d) Work for (b) and (c): Answer: (a) (b) Work for (a) and (b): 19 20 Answer : (a) Source of Variation Factor (Between) Error (Within) Total (b) (c) (d) Work for (a), (b) and (c) Sum of Squares (SS) Degrees of Freedom (df) Mean Square (MS) 42.36 1100.76 N/A