Problem

Local residents are concerned about the speed of cars travelling through their village. They record the speed, in $\text{km h}^{-1}$, of a random sample of 13 cars travelling through their village. The recorded speeds are as follows.

$40,\ 53,\ 59,\ 42,\ 43,\ 48,\ 62,\ 67,\ 46,\ 82,\ 66,\ 45,\ 70$

(a) Construct a $90\%$ confidence interval for the population mean speed of cars passing through the village.

(b) State an assumption that is necessary for the confidence interval found in 1(a) to be valid.