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# HI6007 Statistics for Business Decisions

Published : 03-Sep,2021  |  Views : 10

## Question:

Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviours for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers. The following data are recorded for Consumer information.

 Income (\$1000s) Household Size Amount Charged (\$) Income (\$1000s) Household Size Amount Charged (\$) 54 3 4016 54 6 5573 30 2 3159 30 1 2583 32 4 5100 48 2 3866 50 5 4742 34 5 3586 31 2 1864 67 4 5037 55 2 4070 50 2 3605 37 1 2731 67 5 5345 40 2 3348 55 6 5370 66 4 4764 52 2 3890 51 3 4110 62 3 4705 25 3 4208 64 2 4157 48 4 4219 22 3 3579 27 1 2477 29 4 3890 33 2 2514 39 2 2972 65 3 4214 35 1 3121 63 4 4965 39 4 4183 42 6 4412 54 3 3720 21 2 2448 23 6 4127 44 1 2995 27 2 2921 37 5 4171 26 7 4603 62 6 5678 61 2 4273 21 3 3623 30 2 3067 55 7 5301 22 4 3074 42 2 3020 46 5 4820 41 7 4828 66 4 5149

Required:

1. Use methods of descriptive statistics to summarize the data. Comment on the findings.
2. Develop estimated regression equations, first using annual income as the in- dependent variable and then using household size as the independent variable. Which variable is the better predictor of annual credit card charges Discuss your findings.
3. Develop an estimated regression equation with annual income and household size as the independent variables. Discuss your findings.
4. What is the predicted annual credit card charge for a three-person household with an annual income of \$40,000
5. Discuss the need for other independent variables that could be added to the model. What additional variables might be helpful.

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth medical Center in upstate New York investigated the relationship between geographic location and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression.

The data collected follow; higher test scores indicate higher levels of depression. These data are available on the website that accompanies this text in the file named medical1. A second part of the study considered the relationship between geographic location and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. The levels of depression recorded for this study follow. These data are available on the website that accompanies this text in the file named medical2.

 Florida New York North Carolina Florida New York North Carolina 3 8 10 13 14 10 7 11 7 12 9 12 7 9 3 17 15 15 3 7 5 17 12 18 8 8 11 20 16 12 8 7 8 21 24 14 8 8 4 16 18 17 5 4 3 14 14 8 5 13 7 13 15 14 2 10 8 17 17 16 6 6 8 12 20 18 2 8 7 9 11 17 6 12 3 12 23 19 6 8 9 15 19 15 9 6 8 16 17 13 7 8 12 15 14 14 5 5 6 13 9 11 4 7 3 10 14 12 7 7 8 11 13 13 3 8 11 17 11 11

Required:

1. Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores.
2. Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions
3. Use inferences about individual treatment means where appropriate. What are your conclusions.

 Florida South Wales New York West indies North Carolina Mean 5.55 Mean 8 Mean Standard Error 0.48 Standard Error 0.49 Standard Error Median 6 Median 8 Median Mode 7 Mode 8 Mode Standard Deviation 2.14 Standard Deviation 2.20 Standard Deviation Sample Variance 4.58 Sample Variance 4.84 Sample Variance Kurtosis -1.06 Kurtosis 0.63 Kurtosis Skewness -0.27 Skewness 0.63 Skewness Range 7 Range 9 Range Minimum 2 Minimum 4 Minimum Maximum 9 Maximum 13 Maximum Sum 111 Sum 160 Sum Count 20 Count 20 Count Mean 14.50 Mean 15.25 Mean Standard Error 0.71 Standard Error 0.92 Standard Error Median 14.5 Median 14.5 Median Mode 17 Mode 14 Mode Standard Deviation 3.17 Standard Deviation 4.13 Standard Deviation Sample Variance 10.05 Sample Variance 17.04 Sample Variance Kurtosis -0.34 Kurtosis -0.03 Kurtosis Skewness 0.28 Skewness 0.53 Skewness Range 12 Range 15 Range Minimum 9 Minimum 9 Minimum Maximum 21 Maximum 24 Maximum Sum 290 Sum 305 Sum Count 20 Count 20 Count Groups Count Sum Average Variance Florida 20 290 14.5 10.05 New York 20 305 15.25 17.04 North Carolina 20 279 13.95 8.68 Source of Variation SS df MS F Between Groups 17.03 2 8.517 0.714
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