Genetic evolution is based on mutation. Consequently, one fundamental question in evolutionary biology is the rate of de novo mutations, i. e., those mutations that neither parent possessed. For example, these mutations can occur in the germs cells, the egg or the sperm of the parent. To investigate this question in humans, Kong et al, sequenced the entire genomes of 61 Icelandic trios (mother, father, o spring) and recorded the number of de novo mutations in the o spring. The mean x= 63.95 and the standard deviation s= 14.87.

a)Give a 95% confidence interval for the mean number of mutations

b) mutation rate of one mutation in one-hundred million base pairs would lead to a mean number of de novo mutations of 60. State a hypothesis test for this situation.

c)What does the confidence interval in (a) say about a test with a 5% significance level?

d)Give the t statistic for this situation and state whether or not the test can be rejected at the 1% level. Explain your answer