Smooth Hands is popular across all parts of Singapore where it has been established in the market for several years. They want to know if the number of Smooth Hands jars they sell in a week is related to the number of people living in a particular area. CWC has collected sales data for major areas of Singapore and applied regression analysis to it, using the population of those areas as a predictor. A plot of the data collected is shown in Figure 3.

Smooth Hands is popular across all parts of Singapore where it has been established in the market for several years. They want to know if the number of Smooth Hands jars they sell in a week is related to the number of people living in a particular area. CWC has collected sales data for major areas of Singapore and applied regression analysis to it, using the population of those areas as a predictor. A plot of the data collected is shown in Figure 3.

Figure 3: Scatter plot of population on the x-axis and sales on the y-axis.

1. Describe the relationship between population and sales shown in Figure 3. (2 marks)
2. Shown in Figure 4 is output from a regression analysis on the data plotted in Figure 3. Use the output to perform a hypothesis test to determine if there is a relationship between the two variables. (7 marks)

3. The output in Figure 4 shows a confidence interval for the slope parameter.
   1. Provide the lower and upper limits of the 95% confidence interval and also provide an interpretation of the interval. Ensure you appropriately and accurately word your response. (2 marks)
   2. Explain how this 95% confidence interval is related to the hypothesis test you performed at b). (2 marks)