STATISTICS CALCULATION

QUESTION

Question

In the 1960s and 1970s, drink driving was a common practice in the Australian culture and its seriousness not recognised at the time. Information on road fatalities and alcohol consumption is given in the Data spreadsheet of the file MCD2080_A2_T112.xlsx (Source: http://www.abs.gov.au/statistics Accessed: 7 November 2011). The data collected includes the number of road fatalities in Australia and the amount of alcohol consumption for Australia in litres over the time period 1960 to 1979.

All tables, graphs and comments for this question should be placed in the appropriately labelled spaces in the worksheet Results.

(a)    Which is the independent (or predictor) variable and which is the dependent (or response) variable in this case? Answer in Textbox (a) explaining the reasoning for your choice of variables.

4 marks

(b)    Produce a scatter plot of the data [Graph (b)].  The chart must have an appropriate title and labels. Also you should rescale the graph axes to most clearly display the data. Describe the type of relationship between the variables as shown in the scatterplot. Would a linear regression model be appropriate to model this data? Answer in Textbox (b).

9 marks

Australia was the first country in the world to introduce the compulsory wearing of seatbelts in motor vehicles in 1970. Complete the following questions using only the data prior to the introduction of the compulsory wearing of seatbelts. (i.e. from 1960 to 1969)

(c)    Using the regression function in Excel, generate regression output for the data and place it where indicated in the Results worksheet.

1.                            i.          Write down the line of best fit for the given data from the regression output obtained.  Clearly indicate the variables used in the equation. [(Textbox (c)]
2.                           ii.          State the value of the intercept of the equation correct to two decimal places and interpret this value in Textbox (c). Discuss the validity of the intercept value.
3.                          iii.          State the value of the coefficient of determination correct to three decimal places and explain what information the coefficient of determination gives about the relationship between the variables in Textbox (c).

12 marks

(d)    Investigate whether the data provides statistical evidence of a positive linear relationship between the amount of alcohol consumption and the number of road fatalities. Answer in Textbox (d).

1.                            i.          Give appropriate null and alternative hypotheses. (You are not required to type Greek letters with subscripts. You may use words or symbols instead of Greek letters. For example, H₀ can be written as H_0, and β1 as beta_1, etc.)
2.                           ii.          State the appropriate p-value for this test from the regression output. If the significance level were 1%, would the null hypothesis be rejected? At what levels of significance will the null hypothesis be rejected?
3.                          iii.          Briefly explain what a rejection of the null hypothesis means in this case.

9 marks

(e)    Predict the number of road fatalities (as a whole number) when the amount of alcohol consumption in Australia is:

1.                            i.          80,000 litres
2.                           ii.          120,000 litres

Comment on the reliability of each prediction. Answer in Textbox (e).

8 marks

(f)     Did the introduction of the compulsory wearing of seatbelts have an impact on the number of road fatalities? Answer in Textbox (f) explaining the reasoning for your answer.

3 marks

Presentation: 5 marks (If your presentation is easy to read, you will get these 5 marks.  Ease of reading is assisted by appropriate font size, borders, colour choice and labelling in graphs, and some care in spelling, grammar and punctuation.)

SOLUTION

KI92

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