3 The scatter diagram below illustrates data concerning average annual income per person, \(
) x\(, and average life expectancy, \)y$ years, for 45 randomly selected cities.
\includegraphics[max width=\textwidth, alt={}, center]{464c80be-007b-4d5a-9fe5-2f35100bdea6-3_860_1465_354_244}
- State whether neither variable, one variable or both variables can be considered to be random in this situation.
A student is researching possible positive association between average annual income and average life expectancy. The student decides that the data point labelled A on the scatter diagram is an outlier.
- Describe the apparent relationship between average annual income and average life expectancy for this data point relative to the rest of the data.
The data for point A is removed. The student now wishes to carry out a hypothesis test using the product moment correlation coefficient for the remaining 44 data points to investigate whether there is positive correlation between average annual income and average life expectancy.
- Explain why this type of hypothesis test is appropriate in this situation. Justify your answer.
The summary statistics for these 44 data points are as follows.
\(\sum x = 751120 \sum y = 2397.1 \sum x ^ { 2 } = 14363849200 \sum y ^ { 2 } = 133014.63 \sum x y = 42465962\) - Determine the value of the product moment correlation coefficient.
- Carry out the test at the 1\% significance level.