For each of the following questions:

A) Frame the null and alternative hypothesis. Be sure to define any symbols you use.

B) Specify the most appropriate test statistic that you would use and your reasoning for it. You need to specify the formula only. There is no need to set it up or calculate it. Specify any conditions you may need to check if you had to complete these studies.

1). Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They randomly assign 100 hens between the two feeds and record the number of eggs each hen produces in a month, and then compare the two groups.

2. Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They give all 100 hens the new feed for 2 weeks and the old feed for 2 weeks, randomly selecting which feed the hens get first. They then analyze the differences in production for all 100 hens.

3. Test if a given coin is fair if tossing it 100 times lead to 45 tails.

4. Only about 20% of people who try to quit smoking succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people quit.

5. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 40 years. To test our hypothesis, we select a random sample of 50 men who married for the first time last year, and found that the men in our sample married at an average age of 24.2 years, with a standard deviation of 5.3 years..