1. The candy company that makes M&M's claims that 10% of the M&M's it produces are green. Suppose that the candies are packaged at random in large bags of 200 M&M's. When we randomly pick a bag of M&M's we may assume that this represents a simple random sample of size n = 200. Suppose we wish to test H₀: p = 0.10 versus H_a: p 0.10. Suppose that in a randomly selected bag of M&M's, there are 40 green M&M's. Write the formal (complete) sentence that answers this question.

2. After once again losing a football game to the college'srival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. They test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50. What is the value of the test statistic for this hypothesis test?

3. There is substantial interest in the health benefits of the consumption of high amounts of fiber in diets. A market research team is interested in the public acceptance of a new high-fiber cereal (more than 8 gm of fiber per serving) that is to be marketed. To that end, the researchers selected a random sample of subjects from one region of the country. The selected subjects were provided with two bowls of cereal. One bowl contained the new cereal and the other bowl a well-known and popular cereal. The bowls were presented in random order and subjects asked which cereal they preferred. The study was repeated independently in a second region. In region 1, of the 400 subjects, 220 preferred the new cereal; in region 2, 195 of the 300 subjects indicated a preference for the new cereal.

The researchers wanted to test whether the proportions of consumers who preferred the new high-fiber cereal are the same or different in the two regions. What null and alternative hypotheses should they establish? Write each as the complete verbal statement.

4. A study was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of students was selected from each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Results are presented by the gender of the child in the table below:

	Gender
Goal	Boys	Girls
Make good grades	96	295
Be popular	32	45
Be good in sports	94	40

Write thealternative hypothesisas a complete sentence for aX^2 -Test on the data.

5. A study was performed to examine the personal goals of children in grades4,5,and6.A random sample of students was selected from each of the grades4,5,and6from schools in Georgia.The students received a questionnaire regarding achieving personal goals.They were asked what they would most like to do at school:make good grades,be good at sports,or be popular.Results are presented by the gender of the child in the table below:

	Gender
Goal	Boys	Girls
Make good grades	96	295
Be popular	32	45
Be good in sports	94	40

What is the p-value for the appropriate test from the previous question?

6. After once again losing a football game to the college's rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach.

Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50. Based on the p-value at a 5% significance level, they will reject the null hypothesis; is that true?