2 The directors of a large company believe that there are more computer failures in the Head Office when temperatures are higher. They obtain data for the Head Office for the maximum temperature, \(T ^ { \circ } \mathrm { C }\), and the number of computer failures, \(X\), on each of 12 randomly chosen days.

1. State which of the following words can be applied to \(T\). Dependent Independent Controlled Response The data is summarised as follows.
   \(n = 12 \quad \sum t = 261 \quad \sum x = 41 \quad \sum t ^ { 2 } = 5869 \quad \sum x ^ { 2 } = 311 \quad \sum \mathrm { tx } = 1021\)
2. Calculate the value of the product moment correlation coefficient \(r\).
3. The directors wish to investigate their belief using a significance test at the \(1 \%\) level.
   1. Explain why a 1-tail test is appropriate in this situation.
   2. Carry out the test.
4. One of the directors prefers the temperatures to be given in Fahrenheit ( \({ } ^ { \circ } \mathrm { F }\) ), rather than Centigrade ( \({ } ^ { \circ } \mathrm { C }\) ). The relationship between F and C is \(\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32\).
   State the value of \(r\) that would result from using temperatures in Fahrenheit in the calculation.