Give a reason for using a sample rather than the whole population in carrying out a statistical investigation.
Tennis balls of a certain brand are known to have a mean height of bounce of 64.7 cm , when dropped from a height of 100 cm . A change is made in the manufacturing process and it is required to test whether this change has affected the mean height of bounce. 100 new tennis balls are tested and it is found that their mean height of bounce when dropped from a height of 100 cm is 65.7 cm and the unbiased estimate of the population variance is \(15 \mathrm {~cm} ^ { 2 }\).
(a) Calculate a \(95 \%\) confidence interval for the population mean.
(b) Use your answer to part (ii) (a) to explain what conclusion can be drawn about whether the change has affected the mean height of bounce.