- [Maximum mark: 5]
The temperatures at 5 different locations on a coral reef were measured. The mean of this sample was 20.1 °C and the standard deviation of this sample, sₙ, was 3.2 °C.
(a) Find an unbiased estimate of the population variance. [2]
(b) Assuming that the temperatures are normally distributed, find a 95 % confidence interval for the mean temperature on the coral reef. [2]
(c) Using your answer to part (b), determine if it is plausible that the mean temperature on the coral reef could be 17 °C. [1]