Reference no: EM132858053

Following the enumeration of the chromosomes of many species of mammals, the Swiss genitist Robert Matthey published, in 1956, a histogram of the frequency of diploid numbers of 107 rodent species of the Muridae family. This group of species corresponded roughly to the total number of species described at the time by taxonomists in this family, and for this reason this set of 107 numbers chromosome can therefore be considered to represent the statistical population constituted by the set of chromosomal numbers of all Muridae. Although the chromosomal number of individual organisms is a discontinuous character, the extent of the variation in this data is sufficient for it to be approximately correct to treat this character as continuous. In addition, examination of the histogram of frequencies published by Matthey (1956) suggests that the distribution of the chromosome number looks like the normal distribution.

The following table gives you the main statistics of the sample studied by Matthey:

n = 107

x¯ = 46,9252

Σ (x- x¯)2 = 12195,4

a) Calculate the variance S2, the standard deviation S, the variance of the mean S2 x¯ and the reduced deviation of the mean S x¯

b) We find the diploid number X = 66 in another species of rodent and we ask ourselves if this new individual would belong to a group whose mean µ would differ from that of the population from which the previous sample was taken ie [ H0: X = µ = µ0; H1: X = µ different from µ0]. Test this hypothesis.