8 The following table gives the mean per capita consumption of mozzarella cheese per annum, \(x\) pounds, and the number of civil engineering doctorates awarded, \(y\), in the United States in each of 10 years.
| \(x\) | 9.3 | 9.7 | 9.7 | 9.7 | 9.9 | 10.2 | 10.5 | 11.0 | 10.6 | 10.6 |
| \(y\) | 480 | 501 | 540 | 552 | 547 | 622 | 655 | 701 | 712 | 708 |
- Find the equation of the regression line of \(y\) on \(x\).
You are given that the product moment correlation coefficient is 0.959 .
- Explain whether this value would be different if \(x\) is measured in kilograms instead of pounds.
It is desired to carry out a hypothesis test to investigate whether there is correlation between these two variables.
- Assume that the data is a random sample of all years.
(a) Carry out the test at the \(10 \%\) significance level.
(b) Explain whether your conclusion suggests that manufacturers of mozzarella cheese could increase consumption by sponsoring doctoral candidates in civil engineering.
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