2007 H2 Mathematics

Paper 2 Question 7

A large number of students in a college have completed a geography project. The time, $x$ hours, taken by a student to complete the project is noted for a random sample of $150$ students. The results are summarised by

$\sum x = 4626, \sum x^{2} = 147,691 .$

(a)

Find unbiased estimates of the population mean and variance.

[2]

(b)

Test, at the $5 %$ significance level, whether the population mean time for a student to complete the project exceeds $30$ hours.

[4]

(c)

State, giving a reason, whether any assumptions about the population are needed in order for the test to be valid.

[1]