2020 ACJC P2 Q8

Wally is looking for an investment plan that generates a monthly income of more than \(\$200\). He shortlisted an investment plan whose prospectus promises investors a variable monthly income with a mean of \(\$200\) per month. Wally decides to research further by collecting a random sample of \(36\) of the plan’s past monthly income returns. The monthly income returns, \(\$x\), are summarised as follows.

\(\sum{(x-200)=662.4\,\,\,\,\,\,\,\,\sum{{{(x-200)}^{2}}}}=307141.56\)

1. Test, at the \(10\%\) level of significance, whether Wally should invest in this plan. You should state your hypotheses and define any symbols you use.[6]
2. Explain what is meant by the phrase ‘\(10\%\) significance level’ in the context of this question.[1]