The white \"Spirit\" black bear (or Kermode) Ursusamericanus kermodei, differs from the ordinary blackbear by a single amino acid change in the melanocortin 1receptor gene (MC1R).

In this population, the gene has two forms (or alleles): the\"white\" allele b and the \"black\" allele B. The trait is recessive:white bears have two copies of the white allele of this gene (bb),whereas a bear is black if it has one or two copies of the blackallele (Bb or BB). Both color morphs and all three genotypes arefound together in the bear population of the northwest coast ofBritish Columbia. If possessing the white allele has no effect ongrowth, survival, reproductive success, or mating patterns ofindividual bears, then the frequency of individuals with BB, Bb, orbb allele combinations in the population will follow abinomial distribution (that is BB- 25%, Bb- 50%and bb- 25%). To investigate, Hedrick and Ritland (2011) sampledand genotyped 87 bears from the northwest coast:

42 were BB

24 were Bb

21 were bb

Assume that this is a random sample.

A formal hypothesis test was carried out to compare the observedand expected frequencies of genotypes.

(a)  (null or alternative) hypothesis would be \"Thefrequency distribution of genotypes has a binomial distribution inthe population\"

whereas \"The frequency distribution of genotypes does not have abinomial distribution\" is the  (null or alternative)hypothesis.

(b) The degrees of freedom for the test statistic are .

(c) The calculated chi-square value is  (report to onedecimal place)

(d) The critical chi-square value at alpha =0.05is  (report the whole number from the provided chi-squaredistribution table)

(e) The difference between the observed and expected frequenciesis statistically significant.  (Yes or No)

(f) The calculated chi-square value exceeds the criticalchi-square value corresponding to = 0.05.  (Yes orNo)

(g) The calculated chi-square value exceeds the criticalchi-square value corresponding  to  =0.01.  (Yes or No)