Option #1: Springdale Shopping Survey Instructions The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey can be found in the file CODING. The contingency tables and relative frequency probabilities in this exercise are based on the Springdale Shopping Survey database. Information like that gained from the two parts of this exercise could provide helpful insights into the nature of the respondents, their perceptions, and their spending behaviors. In particular, part 2 focuses on how conditional probabilities related to spending behavior might vary, depending on the gender of the respondent. NOTE: Be sure to use five (5) decimal places for your probabilities in the report, as some of them will be quite small. Do not convert to percentages as we are interested in probabilities only here. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from: SPRSPEND [variable 4] spends at least $15 during a trip to Springdale Mall. DOWSPEND [variable 5] spends at least $15 during a trip to Downtown. WESSPEND [variable 6] spends at least $15 during a trip to West Mall. Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the amount of money a shopper spends during a typical shopping visit. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from: BSTQUALI [variable 11] feels that Springdale Mall has the highest-quality goods. BSTQUALI [variable 11] feels that Downtown has the highest-quality goods. BSTQUALI [variable 11] feels that West Mall has the highest-quality goods. Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the quality of goods offered. Set up a contingency table for the appropriate variables given, and then determine the following probabilities: SPRSPEND and RESPGEND [variables 4 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to Springdale Mall? Is a male more likely or less likely than a female to spend at least $15 during a visit to this area? DOWSPEND and RESPGEND [variables 5 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to Downtown? Is a male more likely or less likely than a female to spend at least $15 during a visit to this area? WESSPEND and RESPGEND [variables 6 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to West Mall? Is a male more likely or less likely than a female to spend at least $15 during a visit to this area? Based on the preceding probabilities, rank the shopping areas where males and females are most likely to least likely to spend $15 or more during a shopping visit. Requirements: Your paper should be 2-3 pages in length (not counting the title page and references page) and cite and integrate at least one credible outside source. The CSU Global Library is a great place to find resources. Your textbook is a credible resource. Include a title page, introduction, body, conclusion, and a reference page. The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic. The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment. The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables or graphs.) Document formatting, citations, and style should conform to CSU Global Writing Center. (Links to an external site.) A short summary containing much that you need to know about paper formatting, citations, and references is contained in the Template Paper (Links to an external site.). Option #2: Probabilities of Graduation and Publication Instructions In the following study, three different universities have been tracking a select group of professors over the course of their employment at that university to determine the number of students who are in a particular professor’s classes, how many of those students have graduated, and if any of them have had their work published. The attached Excel file Probabilities are the totals for each of the professors at the three different universities that participated in the study. The purpose of this study is to find the probabilities of graduation and publication for the students in the different professors’ courses. While a causal relationship may not be found between a professor and student graduation or publication, we need to rank the professors based on the different probabilities found using the data sets as described below. Prepare a report (see below) with your ranking of the professors based on the probabilities and conditional probabilities as well as the analysis of each university. Include the following seven (7) items in table format which is provided in the Probabilities file to support your ranking. NOTE: Be sure to retain and report five (5) decimal places for each of your probabilities. Do not convert your computed probabilities to percentages, as we are only interested in probabilities here. The overall probability of students graduating at each of the three universities. The overall probability of students having a publication at each of the three universities. The overall probability of students having a publication, given that they graduated at each of the three universities. The probability of a student graduating for each professor. The probability of a student having a publication for each professor. The probability of a student having a publication, given that they graduated for each professor. Rank the professors within each university for each of the probabilities in 4-6. Then find the sum of the ranks and determine an overall ranking for each professor. Be sure to critically analyze the above calculations in your body paragraphs, explaining how you found each type of probability and then the results that you obtained. Be sure to also explain your criteria for ranking in steps 4-7, being sure to defend why you chose that particular ranking method, as your way might not be the typical method.

The goal of this assignment is to help you understand the logic underlying the estimation of RSE (Random Sampling Error) based on simulated computation (estimation) using height data. See Excel Sheet 1 on Excel contains 1620 people’s height data These 1620 people’s height are 54 sets of 30 samples – this means that sample size(n) is 30 and you have 54 of them. Therefore, in this assignment we make following assumptions: Height data of 1620 people (54 sets of samples containing 30 people’s height) are population (I know this actually is a set of sample, but we pretend that this is a population: N = 1620) 30 people’s height within each set of sample is a set of sample: therefore sample size is 30 (n n=30) and there are 54 sets of samples. Based on these assumptions, please compute: Population mean (mean of the 1620 people’s height) Sample mean (mean of the 30 people) – please choose a specific sample from 54 samples, and compute the sample mean based on 30 samples in that particular set.Population standard deviation based on 1620 people as population Sample standard deviation (population standard deviation estimated based on your own sample of 30 – so you need to compute the SD on 30 people’s height in your own sample that you chose) Create a sampling distribution of the mean based on these 54 sets of samples and compare the shape (characteristics) of the sampling distribution with population distribution of height that I provided (sheet 2 grouped frequency polygon) by following these steps: Then step 1 compute the mean of 30 people’s height for each of all the 54 sets of samples – so you need 54 sample means for 54 sets of sample step 2 create a group frequency distribution table based on the computed means (54) – this is a grouped frequency table for sampling distribution of the 54 means Compare the shape of frequency distributions between Population of Height (one I provided) and Sampling distribution of the means (54 sets of Means you created). For your reference I am providing the grouped frequency polygon representing the population distribution (the third sheet of the excel) and answer the following questions: What is the relation between population mean and the mean of the 54 means? – same or differentWhich of the two distributions (population distribution of 1620 height data vs sampling distribution of the 54 means) has a narrower distribution clustered around the population mean? to what extent, the observation of the above two (a and b) aspects of the sampling distribution lend support to the Central Limit Theorem? – this requires you read CLM and understand it. RSE as difference between your own sample mean and the mean of the sampling distribution of mean (average of the 54 sets of sample mean)RSE as Standard Error of the Mean which is the Standard Deviation computed based on sampling distribution of the mean – this means computing a SD based on 54 sample means. For this use the sampling distribution of the mean that you created in the above (you need to use population St Dev computation function in Excel – see below). RSE as Standard Error of the Mean approximated by population standard deviation (based on 1620 data) divided by the square root of n (n=30) RSE as Standard Error of the Mean approximated by sample standard deviation (based on your own sample of n=30) (use of n-1 in denominator – sample standard deviation in Excel – see below) divided by the square root of n (n=30)(This is a bonus point of 5 on top of 30) I assume that 6-3 and 6-4 are different even though they are supposed to be similar according to the lecture. Speculate on the reason why they are different.Based on what you have learned on the four different approaches of estimating RSE, they should be the same. But they are different in this one. Why? Hint: the nature of the sample (30 people’s height)? You can include any questions or comments based on this process. Your points is not entirely based on whether your answer is correct; it is mainly based on evidence of THINKING you put here. 6 ) Estimate the Random Sampling Error in the following four different ways based on your understanding of the definition of RSE we just covered in the class: In computing Means and SD, use excel’s computational functions: For mean (average) see: https://www.youtube.com/watch?v=5_OHS-18RbU\ For standard deviation see: https://www.youtube.com/watch?v=uZWQXQG37Zs There are STD. P (population where the denominator is n) and STD.S (sample where the denominator is n-1). Be careful to use appropriate one. You should, by now, know which one to use when. If you have question on this, please send me an email. In sum your assignment needs to address all these questions Population mean Sample mean Population standard deviation Sample standard deviation (population standard deviation estimated based on your own sample) RSE as difference between your sample mean and the mean of the sampling distribution of mean (average of the 54 sets of sample mean) RSE as Standard Error of the Mean which is Standard Deviation computed on the sampling distribution of the mean. RSE as Standard Error of the Mean approximated by population standard deviation divided by the square root of n (n=30) RSE as Standard Error of the Mean approximated by sample standard deviationofyour own sample) divided by the square root of n (n=30)(bonus points) consideration of why 6-3 and 6-4 are different. 5-aWhat is the relation between population mean and the mean of the 54 means? 5-b. Which of the two distributions (population vs sampling distribution of the means) has a narrower distribution clustered around the population mean? 5-c.To what extent, the observation of the above two (a and b) aspect of the sampling distribution lend support to the Central Limit Theorem?