2019 H2 Mathematics Paper 2 Question 9

Hypothesis Testing

Answers

(i)

The manager should carry out a 2-tail test as, in testing whether the mean resistance is in fact 750, the actual population mean resistance could be greater or less than 750.

${\textrm{H}_0: \mu = 750}$
${\textrm{H}_1: \mu \neq 750}$

(ii)

{p\textrm{-value} = 0.0897}

There is insufficient evidence at the

{5\%}

level of significance to conclude whether the mean resistance of the resistors is

{750}

ohms

(iii)

We will need to take a larger sample of size at least

{30.}

Since the population distribution of the

{1250}

ohm resistors is unknown, in order for the sample mean test statistic

{\overline{X}}

to be normally distributed (approximately) to carry out at

{Z\textrm{-}}

test, we will need a large sample size of at least

{30}

so that the Central Limit Theorem can be applied.

Full solutions

(i)

The manager should carry out a 2-tail test as, in testing whether the mean resistance is in fact 750, the actual population mean resistance could be greater or less than 750.

{\blacksquare}

Let

{\mu}

denote the population mean resistance of the resistors,

{X}

denote the random variable of the resistance of the resistors,

{\overline{x}}

denote the mean resistance of the sample of

{8, }

and

{\mathrm{H}_0}

and

{\mathrm{H}_1}

be the null and alternative hypothesis respectively.

{\textrm{H}_0: \mu = 750}

{\textrm{H}_1: \mu \neq 750 \; \blacksquare}