Question 4 - A-Level Maths

Exam Board	Edexcel
Module	S3 (Statistics 3)
Year	2011
Session	June
Topic	Hypothesis test of a normal distribution

A shop manager wants to find out if customers spend more money when music is playing in the shop. The amount of money spent by a customer in the shop is \(\pounds x\). A random sample of 80 customers, who were shopping without music playing, and an independent random sample of 60 customers, who were shopping with music playing, were surveyed. The results of both samples are summarised in the table below.

	\(\sum x\)	\(\sum x ^ { 2 }\)	Unbiased estimate of mean	Unbiased estimate of variance
Customers shopping without music	5320	392000	\(\bar { x }\)	\(s ^ { 2 }\)
Customers shopping with music	4140	312000	69.0	446.44

Find the values of \(\bar { x }\) and \(s ^ { 2 }\).
Test, at the \(5 \%\) level of significance, whether or not the mean money spent is greater when music is playing in the shop. State your hypotheses clearly.