Statistics

Discussion Questions

1.Locate a visual presentation of data in a newspaper, magazine, or Internet article and if possible attach it to your post or give a link to it so that we may find it.  Outline what is being represented in the information and then determine whether or not any abuses of visual displays are being used to mislead the viewer.  Argue your point why you think this and, if there are abuses, what they could do to make it correct.

2. Coefficient of variation and standard deviation are two measures of dispersion or spread among data values. Provide two different sets of ten data points each as examples. Explain which of the two mentioned measures can more accurately specify which of these two data sets have more spread or variability in their data values. Calculate the standard deviation and coefficient of variation for each data set to clarify your explanation.

3. Do you use probability in your profession or real life? You most likely do. Give an example of how you have used probability in your life. Be sure to show how you calculated it. Did the resulting outcome of the event back up your probability that you calculated? If not what were the reasons why?

4. Provide an example of a binomial random variable as these apply to something in your life. Specifically, provide a ”real world” example of a random variable that would satisfy the characteristics of the binomial. Be specific in your reply as it relates to your life.

5. When one thinks of the normal distribution the first thing that comes to mind is the bell curve and grades. While this is one example of a normal curve that is widely recognized, it is not the only one. Try to come up with a unique normal distribution that your classmates have not posted already. Explain your curve with all the details you could find such as the mean and standard deviation. What do the areas in the intervals µ – σ to µ + σ, µ – 2σ to µ + 2σ and µ – 3σ to µ + 3σ represent as far as areas under the normal curve? If you have the mean and standard deviation, calculate what the actual intervals are for your curve. Please include any citations on where you obtained your data for the curve

6. One can calculate the 95% confidence interval for the mean with the population standard deviation known. This will give us an upper and a lower confidence limit. What happens if we decide to calculate the 99% confidence interval? Describe how the increase in the confidence level has changed the width of the confidence interval. Do the same for the confidence interval set at 80%. If it helps you to visualize or describe any of the above, you can use an example and give real values for the intervals in your post.

7. Share with your peers the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Additionally, identify the Type I and Type II Errors that could occur with your decision‐making process.

8. Regression analysis can be used to analyze how a change in one variable impacts the other variable, such as an increase in marketing budget increasing sales. Find a unique area of your life where one variable impacts the other variable that are both measurable and do a regression analysis on it. Share your results and make any comments as to whether or not there is a possibility of potential problems (causation or extrapolation) with your results.

1.

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.

We will concentrate on variables 18–25, which reflect how important each of eight different attributes is in the respondent’s selection of a shopping area. Each of these variables has been measured on a scale of 1 (the attribute is not very important in choosing a shopping area) to 7 (the attribute is very important in choosing a shopping area). The attributes being rated for importance are listed below. Examining the relative importance customers place on these attributes can help a manager “fine-tune” his or her shopping area to make it a more attractive place to shop.

18 Easy to return/exchange goods 19 High quality of goods 20 Low prices 21 Good variety of sizes/styles 22 Sales staff helpful/friendly 23 Convenient shopping hours 24 Clean stores and surroundings 25 A lot of bargain sales

1. Perform the following operations for variables 18–25:

1. Compute descriptive statistics (5-number summary, mean, mode, range and standard deviation) for each variable along with an explanation of what the descriptive statistics tell us about the variable.

2. Are there any data points for any of the variables that can be considered outliers? If there are any outliers in any variable, please list them and state for which variable they are an outlier. Use the z-score method to determine any outliers for this question.

2. Based on the results for question 1, which attributes seem to be the most important and the least important in respondents’ choice of a shopping area? Which items from #1 did you use to decide on the least and most important attributes, and why?

3. Determine the correlation coefficient between variable 19 and variables 21 - 25. Please provide an explanation of the relationships.

Paper Requirements

Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page too. Please include any tables of calculations, calculated values and graphs associated with this problem in the body of your assignment response.

NOTE: You MUST submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.

2.

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.

1. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from

1. [variable 4] spends at least $15 during a trip to Springdale Mall.

2. [variable 5] spends at least $15 during a trip to Downtown.

3. [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.

2. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from

1. [variable 11] feels that Springdale Mall has the highest-quality goods.

2. [variable 11] feels that Downtown has the highest-quality goods.

3. [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.

3. Set up a contingency table for the appropriate variables given, and then determine the following probabilities:

1. [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?

2. [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?

3. [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.

Paper Requirements

Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page too. Please include any tables of calculations, calculated values and graphs associated with this problem in the body of your assignment response.

NOTE: You MUST submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.

3. 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.

In this exercise, some of the estimation techniques presented in the module will be applied to the Springfield Shopping survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community, and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results.

Managers associated with shopping areas like these find it useful to have point estimates regarding variables describing the characteristics and behaviors of their customers. In addition, it is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the benefit of the techniques presented in this module and applied here.

1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement.

2. Determine the point estimate, then construct the 95% confidence interval for μ7=  the average attitude toward Springdale Mall.

3. Repeat part (a) for μ8 and μ9, the average attitudes toward Downtown and West Mall, respectively.

2. Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate, construct the 95% confidence interval for π26= the population proportion of males.

3. Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate, and then construct the 95% confidence interval for π28 = the population proportion in the “single or other” category.

4. Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of error of 0.05 for each mall. If the managers want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample size be for each mall?

Paper Requirements

. Items that should be included, at a minimum, are a title page, an introduction, a body that answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page too. Please include any tables of calculations, calculated values and graphs associated with this problem in the body of your assignment response.

NOTE: You MUST submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.