8. Observations have been made over many years of \(T\), the noon temperature in \({ } ^ { \circ } \mathrm { C }\), on 21 st March at Sunnymere. The records for a random sample of 12 years are given below.
5.2, 3.1, 10.6, 12.4, 4.6, 8.7, 2.5, 15.3, -1.5, 1.8, 13.2, 9.3.

1. Find unbiased estimates of the mean and variance of \(T\). Over the years, the standard deviation of \(T\) has been found to be 5.1.
2. Assuming a normal distribution find a \(90 \%\) confidence interval for the mean of \(T\).
   (5) A meteorologist claims that the mean temperature at noon in Sunnymere on 21st March is \(4 ^ { \circ } \mathrm { C }\).
3. Use your interval to comment on the meteorologist's claim.