Some critics of television complain that the amount of violence shown on television 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 analyse this belief, a researcher plans to survey a sample of families across the country.

Part A [0.5 + 0.5 + 0.5 = 1.5 marks]

Briefly explain

a What type of survey method could the researcher use and why?

b What sampling method could the researcher use to select his/her sample and why?

c What kind of issues could the researcher face in this data collection?

Suppose the researcher collected data from 430 randomly selected families. For each family, the total debt (in $) and the number of hours the television is turned-on (TV Hours) per week were recorded. The data are stored in file TVDEBT.xlsx and available in the course website under Assessment. Using this data and EXCEL, answer the Parts B, C and D below.

Part B [0.5 + 1.5 = 2 marks]

First, the researcher wishes to use the graphical descriptive methods to present the data for the two variables.

d He suggests using 10 classes such as class intervals 0-6, 6-12, 12-18, .... for the TV Hours variable and class intervals 0-30000, 30000-60000, 60000-90000, .... for the Total Debt variable. Explain how he could have decided on the number of classes as 10.

e Use appropriate BIN values to draw histograms for the two variables and comment on the shape of the two distributions (Hint: draw the frequency polygon as well).

Part C [2 + 1.5 = 3.5 marks]

Second, the researcher wishes to use the numerical descriptive measures to summarize the data.

f 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.

g Use five of the above summary measures to represent the summary information in a box plot for each variable (hand drawn and scanned is OK). Comment on the outliers (if any).

Part D [1 + 1 + 1= 3 marks]

Third, the researcher wishes to use graphical descriptive method and a numerical descriptive measure to analyse the strength of the linear relationship between the two variables.

h Use an appropriate plot to show the relationship between variables, Total Debt and TV Hours.

i Compute a measure of the direction and strength of a linear relationship between the two variables. Interpret this value.

j Comment on thesociologist's theory that 'people who watch television frequently are exposed to many commercials, which in turn lead them to buy, resulting in increasing debt'.