4. A recent census in the U.K. revealed that the heights of females in the U.K. have a mean of 160.9 cm . A doctor is studying the heights of female Indians in a remote region of South America. The doctor measured the height, \(x \mathrm {~cm}\), of each of a random sample of 30 female Indians and obtained the following statistics. $$\Sigma x = 4400.7 , \quad \Sigma \mathrm { x } ^ { 2 } = 646904.41 .$$ The heights of female Indians may be assumed to follow a normal distribution.
The doctor presented the results of the study in a medical journal and wrote 'the female Indians in this region are more than 10 cm shorter than females in the U.K.'

1. Stating your hypotheses clearly and using a \(5 \%\) level of significance, test the doctor's statement.
   (6) The census also revealed that the standard deviation of the heights of U.K. females was 6.0 cm .
2. Stating your hypotheses clearly test, at the \(5 \%\) level of significance, whether or not there is evidence that the variance of the heights of female Indians is different from that of females in the U.K.
   (6)