5 Rebekah is investigating the distances, \(X\) light years, between the Earth and visible stars in the night sky.
She determines the distance between the Earth and a star for a random sample of 100 visible stars.
The summarised results are as follows:
$$\sum x = 35522 \quad \text { and } \quad \sum x ^ { 2 } = 32902257$$
5
- Calculate a 97\% confidence interval for the population mean of \(X\), giving your values to the nearest light year.
5 - Mike claims that the population mean is 267 light years.
Rebekah says that the confidence interval supports Mike's claim.
State, with a reason, whether Rebekah is correct.