It is known that 62% of Americans and 59% of Canadians eat red meat at least three times a week. A US environmental protection group thinks these proportions are actually closer together. The group took a random sample of 1,000 Americans and a random sample of 1,000 Canadians and asked them how many times a week they eat red meat. The sampling distribution of p hat Subscript a Baseline minus p hat Subscript c is approximately Normal with a mean of 0.03 and a standard deviation of 0.0219. P(p hat Subscript a Baseline minus p hat Subscript c < 0) = 0.085 Does the sample result provide convincing evidence against the group’s claim? No, there is only a 3% difference between the two samples. No, the difference between the sample result and what we expected is not extreme enough (0.085 > 0.05). Yes, there is a very small chance of seeing the sample result. It is unlikely to occur by chance alone. Yes, the probability of seeing the sample result is so far from what we expected that the probability of it occurring by chance alone is very unlikely.
