In problem 8.15 the nutritionist was interested in knowing if the rate of vegetarianism in American adults has increased. She carried out a hypothesis test and found that the observed value of the test statistic was 2.77. We can calculate that the p-value associated with this is 0.0028, which is very close to 0. Explain the meaning of the p-value in this context. Based on this result, should the nutritionist believe the null hypothesis is true?

Problem 8.15

In 2016 the Harris poll estimated that 3.3% of American adults are vegetarian. A nutritionist thinks this rate has increased. The nutritionist samples 150 American adults and finds that 11 are vegetarian.

a. What is p̂, the sample proportion of vegetarians?

b. What is p₀, the hypothetical proportion of vegetarians?

c. Find the value of the test statistic. Explain the test statistic in context.