A researcher is using the statistical investigation process to investigate a possible relationship between average number of minutes per day a person spends watching television, and the average number of minutes per day the person spends exercising.
- State the statistical question being posed. (1 mark)
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Participants were asked to record the number of minutes they spent watching television each day and the number of minutes they spent exercising each day. The averages for each participant were recorded and graphed, and a line of best fit was included.
- From the graph, identify the dependent variable. (1 mark)
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- Describe the bivariate dataset in terms of its form and direction. (2 marks)
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- The points \((0, 70)\) and \((60, 10)\) lie on the line of best fit. By first plotting these points on the graph, find the gradient and the \(y\)-intercept of the line of best fit. (3 marks)
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- Explain why it is NOT appropriate to extrapolate the line of best fit to predict the average number of minutes of exercise per day for someone who watches an average of 2 hours of television per day. (1 mark)
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a. \(\text{How does the average daily time spent watching television}\)
\(\text{relate to the average daily time spent exercising?}\)
b. \(\text{Dependent variable:}\)
\(\text{Average minutes per day exercising, or }y.\)
c. \(\text{Form: Linear}\)
\(\text{Direction: Negative}\)
d.
\(y-\text{intercept = 70}\)
\(\text{Gradient}=\dfrac{\text{rise}}{\text{run}}=\dfrac{-60}{60}=-1\)
e. \(\text{The extrapolation of the graph past 70 minutes produces}\)
\(\text{negative average minutes per day exercising (impossible).}\)
