Gregor Mendel (1822–1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or wrinkled. Mendel predicted a ratio of 3 smooth peas for every 1 wrinkled pea. In one experiment, he observed 423 smooth and 133 wrinkled peas. Assume that the conditions for inference are met.

a. State appropriate hypotheses for testing Mendel’s claim about the true proportion of smooth peas.

b. Calculate the standardized test statistic and P-value.

c. Interpret the P-value. What conclusion would you make?