Question

If two heterozygous parents (i.e., both Aa) mate, they produce offspring in the expected Mendelian proportions (i.e., 1/4 AA, 1/2 Aa, 1/4 aa). We observe a big Drosophila family of 40 offspring of which 7 are aa.

i) Construct a 95% confidence interval on the observed proportion of aa offspring (7/40). What does this confidence interval tell us about our null hypothesis? Hint: our null hypothesis is that Mendelian laws have not been violated.

ii) Are 7 or fewer offspring statistically consistent with Mendelian expectations? Hint: figure out the probability of observing 7 or fewer offspring in such a family, if Mendelian laws have not been violated.

iii) How few offspring of type aa would we have to observe in order to be suspicious that Mendelian proportions are being violated? Is your answer a test of a one-tailed hypothesis or a two-tailed hypothesis?

Answer 1

i) The 95% interval confidence is 0.0574-0.293 (see picture below for all the steps)

This interval confidence tells us that the null hypothesis is accepted because the proportion of aa observed (7/40=0.175) is within this interval.

ii) the probability is 0.1357 (see picture below for the math)

iii) If we observe 2 samples with aa genotypes we can suspect that Mendelian proportions are violated. That is calculated based on the lower limit in the confidence interval (0.057). That is the minimum proportion of aa = (40*0.057=2.2). It is a one-tailed hypothesis