- Roxane, a scientist, carries out an investigation into the fat content of different brands of crisps.
Roxane took random samples of different brands of crisps and recorded, in grams, the fat content ( \(x\) ) of a 30 gram serving.
The table below shows some results for just two of these brands.
| Brand | \(\sum x\) | \(\sum \boldsymbol { x } ^ { \mathbf { 2 } }\) | \(\bar { x }\) | \(s\) | Sample size |
| A | 350 | 1753.9744 | 5.0 | 0.24 | 70 |
| B | 331.5 | 1694.65 | \(\alpha\) | β | 65 |
- Calculate the value of \(\alpha\) and the value of \(\beta\)
Roxane claims that these results show that the crisps from brand A have a lower fat content than the crisps from brand B , as the mean fat content for brand A is, statistically, significantly less than the mean fat content for brand B .
- Stating your hypotheses clearly, carry out a suitable test, at the \(5 \%\) level of significance, to assess Roxane's claim.
You should state your test statistic and critical value. - For the test in part (b), state whether or not it is necessary to assume that the fat content of crisps is normally distributed. Give a reason for your answer.
- State an assumption you have made in carrying out the test in part (b).