ALY 6015 Intermediate Analytics Module 5 Assignment

Class ALY6015 – Intermediate Analytics

Module 5 Assignment: Nonparametric Methods and Sampling

Overview and Rationale

In this assignment, you will use your knowledge of nonparametric statistical methods and sampling to solve various types of problems.

Course Outcomes

This assignment is directly linked to the following key learning outcomes from the course syllabus:

● State the advantages and disadvantages of nonparametric methods.

● Test hypotheses, using the following methods: sign test, Wilcoxon rank sum test, signed-rank test, Kruskal-Wallis test, and the runs test.

● Compute the Spearman rank correlation coefficient.

● Demonstrate a knowledge of the four basic sampling methods.

● Recognize faulty questions on a survey and other factors that can bias responses.

● Solve problems, using simulation techniques.

Submission Requirements

1. Complete paperwork in MS Word format (.docx) must include:

● Title Page

o Your name (as registered in Canvas)

o Assignment name

o Class number, name and CRN Number

o Your contact information (NEU email)

● Assignment summary section.(Explain assignment summary, plans, goals, dataset).

● Each step of the research with supporting screenshots, charts, results generated by R code.

● Explain each screen shot from the data standpoint.

● Each output generated by R code must be present and explained in the paperwork.

● Each output, chart, table, screenshot shown in the paperwork must have corresponding R code that generates it.

● Final conclusions section. (Explain if goals were achieved as expected or not, summary of you findings about analyzed data).

● References (optional)

2. Complete R code file meet the following criteria:

● Submitted in R script (.r file format). Only .r file format will be accepted.

● Each line of code must be commented. (Explain why do you execute this line of code, not what the command does).

● Code must be runnable on any computer. Any errors in executing R code will results in significant points deduction. (Follow the guidelines provided in the class and user R code examples provided in Canvas)

3. Submit dataset(s) used in the research.

Assignment summary

Follow the instructions section and complete each task utilizing the nonparametric statistical methods and techniques.

Instructions

Perform these steps:

1. State the hypotheses and identify the claim.

2. Find the critical value(s)

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified. Assume all assumptions are met.

Task 1: Game Attendance

An athletic director suggests the median number for the paid attendance at 20 local football games is 3000. The data for a random sample are shown. At α = 0.05, is there enough evidence to reject the claim? If you were printing the programs for the games, would you use this figure as a guide?

6210	3150	2700	3012	4875
3540	6127	2581	2642	2573
2792	2800	2500	3700	6030
5437	2758	3490	2851	2720

Source: Pittsburgh Post Gazette

Task 2: Lottery Ticket Sales

A lottery outlet owner hypothesizes that she sells 200 lottery tickets a day. She randomly sampled 40 days and found that on 15 days she sold fewer than 200 tickets. At α = 0.05, is there sufficient evidence to conclude that the median is below 200 tickets?

Use the Wilcoxon rank sum test. Assume that the samples are independent. Also perform each of these steps.

1. State the hypotheses and identify the claim.

2. Find the critical value.

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified. Assume all assumptions are valid.

Task 3: Lengths of Prison Sentences

A random sample of men and women in prison was asked to give the length of sentence each received for a certain type of crime. At α = 0.05, test the claim that there is no difference in the sentence received by each gender. The data (in months) are shown here.

Males	8	12	6	14	22	27	32	24	26	19	15	13
Females	7	5	2	3	21	26	30	9	4	17	23	12	11	16

Source: Based on information from the National Highway Traffic Safety Administration.

Task 4: Winning Baseball Games

For the years 1970–1993 the National League (NL) and the American League (AL) (major league baseball) were each divided into two divisions: East and West. Below are random samples of the number of games won by each league’s Eastern Division. At α = 0.05, is there sufficient evidence to conclude a difference in the number of wins?

NL	89	96	88	101	90	91	92	96	108	100	95
AL	108	86	91	97	100	102	95	104	95	89	88	101

Task 5: Wilcoxon Signed-Rank Test.

Use Critical Values for the Wilcoxon Signed Rank Test Table (Table K). Determine whether the null hypothesis should be rejected for the following:

1.  = 13, n = 15, α = 0.01, two-tailed

2.  = 32, n = 28, α = 0.025, one-tailed

3.  = 65, n = 20, α = 0.05, one-tailed

4.  = 22, n = 14, α = 0.10, two-tailed

Use the Kruskal-Wallis test and perform these steps.

1. State the hypotheses

2. Find the critical value.

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

Task 6: Mathematics Literacy Scores

Through the Organization for Economic Cooperation and Development (OECD), 15-year-olds are tested in member countries in mathematics, reading, and science literacy. Listed are randomly selected total mathematics literacy scores (i.e., both genders) for selected countries in different parts of the world. Test, using the Kruskal-Wallis test, to see if there is a difference in means at α = 0.05.

Western Hemisphere	Europe	Eastern Asia
527	520	523
406	510	547
474	513	547
381	548	391
411	496	549

Source: National Center for Education Statistics

Perform these steps.

1. Find the Spearman rank correlation coefficient.

2. State the hypotheses.

3. Find the critical value. Use α = 0.05.

4. Make the decision.

5. Summarize the results.

Task 7: Subway and Commuter Rail Passengers

Six cities are randomly selected, and the number of daily passenger trips (in thousands) for subways and commuter rail service is obtained. At α = 0.05, is there a relationship between the variables? Suggest one reason why the transportation authority might use the results of this study.

City	1	2	3	4	5	6
Subway	845	494	425	313	108	41
Rail	39	291	142	103	33	38

Source: American Public Transportation Association.

Use random numbers to simulate the experiments. The number in parentheses is the number of times the experiment should be repeated.

Task 8: Prizes in Caramel Corn Boxes

A caramel corn company gives four different prizes, one in each box. They are placed in the boxes at random. Find the average number of boxes a person needs to buy to get all four prizes. (40)

Task 9: Lottery Winner

To win a certain lotto, a person must spell the word big. Sixty percent of the tickets contain the letter b, 30% contain the letter i, and 10% contain the letter g. Find the average number of tickets a person must buy to win the prize. (30)