A survey was completed by 446 students in introductory statistics courses at a large university in the fall of 2003. We will consider students to never eat meat if they answered "yes" (as opposed to "no" or "sometimes") to a question that asked if they were vegetarian.
a. Use software to access the survey data and produce a 95% confidence interval for the proportion of all students who never eat meat, assuming the surveyed students were a representative sample.
b. The proportion of adult Americans who never eat meat is reported to be 0.03. Does your interval contain 0.03?
c. Test whether the proportion who never eat meat in the larger population from which surveyed students were sampled could equal 0.03. Draw your conclusions, using 0.05 as the cutoff for a small P-value.
d. Explain how your answers to parts (b) and (c) are consistent with one another.
e. Report the P-value if you had tested against the one-sided alternative that proportion of all such students who never eat meat was greater than 0.03.