Hypothesis testing

Question code: 24067V3495

Question 2701

A large number of students prepare for a national examination. The time,

{x}

hours, taken by a student to prepare for the examination is noted for a random sample of 100 students. The results are summarised by

\sum x = 3044, \quad \sum x^2 = 93090.

(i)

Find unbiased estimates of the population mean and variance.

(ii)

A hypothesis test is conducted, and there was sufficient evidence at the

{\alpha \%}

significance level to conclude that the population mean time for a student to prepare for the examination is 30 hours. Find the range of possible values of

{\alpha.}

(iii)

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

Answer

(i)

{\overline{x} = 30.44, s^2 = 4.35.}

(ii)

(a)

\alpha \geq 3.49

(b)

No assumptions are needed about the population. This is because, as

{n=100}

is large, by the Central Limit Theorem,

{\overline{X}}

is normally distributed approximately so no further assumptions on the population are needed.

Question code: 24067V3495