contributes to violence in our society. Others point out that television contributes to the high level of obesity among children. Now, we may have to add financial problems to the list. A sociologist theorised that people who watch television frequently are exposed to many commercials, which in turn lead them to buy, resulting in increasing debt. To test this belief, a researcher plans to survey a sample of families across the country.
QUESTION
Briefly explain (using no more than 150 words in total for this Question)
(a) What type of survey method the researcher could use and why?
(b) What sampling method could the researcher use to select his/her sample and why?
(c) What are the variables the researcher should consider collecting data for the purpose of the analysis and why? Identify the data type(s) for the variables.
(d) What kind of issues the researcher may face in this data collection?
Suppose the researcher collected data from 430 randomly selected families. For each family, the total debt and the number of hours the television is turned-on per week were recorded. The data are stored in file TVDEBT.XLS which will be available in the "OTHER RESOURCES" section of the IBA134 unit website. Using this data and EXCEL, answer the questions below.
QUESTION
First, the researcher wishes to use the graphical descriptive methods to present the data.
(a) He suggests using 10 classes such as class intervals 0-6, 6-12, 12-18, ... for one variable and class intervals 0-30000, 30000-60000, 60000-90000, .... , for the other variable. Explain how he could have decided on the number of classes as 10 and the above class intervals.
(b) Use appropriate BIN values to draw a histogram for each variable and comment on the shape of the two distributions.
(c) Use an appropriate plot to investigate the relationship between the two variables. Briefly explain the selection of each variable on the X and Y axes and why? On the same plot, fit a linear trend line including the equation and the coefficient of determination.
QUESTION
Second, the researcher wishes to use the numerical descriptive measures to summarize the data.
(a) Prepare a numerical summary report about the data on the two variables the researcher has considered by including the summary measures, mean, median, range, variance, standard deviation, smallest and largest values and the three quartiles, for each variable.
(b) Use five of the above summary measures to represent the summary information in a box plot for each variable.
(c) Compute a numerical summary measure to measure the strength of the relationship between the two variables. Interpret this value.
QUESTION
The researcher wishes to estimate the population means for the two variables under consideration using the sample data.
(a) Compute the best point estimates for the mean of the two variables and their standard errors.
(b) Construct a 95% interval estimate for the population mean of each of the two variables.
(c) Explain what would happen to the two interval estimates in 4(b) above if we use a level confidence 90% instead of 95%. Justify your answer by re-calculating the 90% interval estimates for the population mean of the two variables.
QUESTION
The researcher wishes to test hypotheses about the population means for the two variables under consideration using the sample data.
(a) The researcher believes that the average television time per week is more than 25 hours. How do you test his believe? Is there any evidence for his believe? Use a 5% level of significance.
(b) The researcher believes that the average debt is less than $150,000. How do you test his believe? Is there any evidence for his believe? Use a 5% level of significance.
QUESTION
The researcher considers using regression analysis to establish a linear relationship between the two variables.
(a) What is his dependent variable and independent variable? Why?
(b) Estimate a simple linear regression model and present the estimated linear equation. Interpret the coefficient estimates of the linear relationship.
(c) Calculate the predicted debt level for a family whose television time is 40 hours per week.
(d) Using your answer in part 6(c), calculate the residual debt for a family whose television time is 40 hours per week and debt level is $81,708.
(e) Interpret the R-squared value.