6 Nassa is researching the lengths of a particular type of snake in two countries, \(A\) and \(B\).
- He takes a random sample of 10 snakes of this type from country \(A\) and measures the length, \(x \mathrm {~m}\), of each snake. He then calculates a \(90 \%\) confidence interval for the population mean length, \(\mu \mathrm { m }\), for snakes of this type, assuming that snake lengths have a normal distribution. This confidence interval is \(3.36 \leqslant \mu \leqslant 4.22\).
Find the sample mean and an unbiased estimate for the population variance.
- Nassa also measures the lengths, \(y \mathrm {~m}\), of a random sample of 8 snakes of this type taken from country \(B\). His results are summarised as follows.
$$\sum y = 27.86 \quad \sum y ^ { 2 } = 98.02$$
Nassa claims that the mean length of snakes of this type in country \(B\) is less than the mean length of snakes of this type in country \(A\). Nassa assumes that his sample from country \(B\) also comes from a normal distribution, with the same variance as the distribution from country \(A\).
Test at the \(10 \%\) significance level whether there is evidence to support Nassa’s claim.
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