Gregor Mendel has been called the "father of genetics," having formulated laws of inheritance even before the function of DNA was discovered. In one famous experiment with peas, he crossed pure breeds of tall and dwarf pea plants. The first-generation pea plants were all tall. In the second generation (F2), he obtained 787 tall plants and 277 dwarf plants. Mendel's first law of inheritance is a model with a dominant and a recessive phenotype. The first law says that we can expect a 3:1 ratio, that is, 3/4 with the dominant and 1/4 with the recessive phenotype, in F2.
(a) Are the conditions for a chi-square goodness-of-fit test satisfied?
(b) What are the null and alternative hypotheses for this test?
(c) What are the expected counts under the null hypothesis?
(d) Compute the chi-square statistic and use software or Table D to find the P-value. What can you conclude? Do these data support Mendel's first law?