A sociologist is studying how much junk food teenagers eat. A random sample of 100 female teenagers and an independent random sample of 200 male teenagers were asked to estimate what their weekly expenditure on junk food was. The results are summarised below.
\(n\)
mean
s.d.
Female teenagers
100
\(\pounds 5.48\)
\(\pounds 3.62\)
Male teenagers
200
\(\pounds 6.86\)
\(\pounds 4.51\)
Using a 5\% significance level, test whether or not there is a difference in the mean amounts spent on junk food by male teenagers and female teenagers. State your hypotheses clearly.
Explain briefly the importance of the central limit theorem in this problem.