For each question below, identify which test (or corresponding confidence interval) to use. The appropriate method should be one of the tests from one sample or two sample inference, or one-way ANOVA. Also write the appropriate null and alternative hypothesis. 

1.   20 mice were divided into two groups of 10 and each group were fed one of two diets, a low fat or a high fat diet. Weight measurements were taken before and after the study. For each mouse, the weight gain during the study was measured. We want to test whether there is a significant difference in the weight gain of mice across the two diet groups. 

2.   A study explores the dietary quality of the police officers working in  Chicago, Illinois. Data were collected on 12 Chicago police officers who are willing to participate by completing a four-day food record, including 2 days on duty and 2 days off duty. This food record for each officer is then analyzed on the computer and given a dietary quality score between zero and 100. The closer to 100, the better the quality of the diet. The study wants to construct a 95% confidence interval for the dietary quality score of the police officers in Chicago. 

3.   Clomiphene Citrate (Clomid) is a Serum Estrogen Receptor Modulator class of drug used as a first line treatment in anovulatory women. It has not, however been thoroughly explored in mares. To understand whether oral administration of Clomid increase follicle recruitment, 20 mares were used to perform an experiment (10 control and 10 treatment). For both groups, follicle number was measured post treatment. 

4.   Consider data from a study trying to understand the effect of maternal parenting style on the children’s ability to sit still during a class lesson. A classroom of 22 children is observed during a 30-minute classroom activity. Children’s level of sitting  still is measured by observer observation in minutes and seconds. Maternal parenting style is grouped based on a parent self-report questionnaire that asks how the parent would react in specific situations. The responses to these questions are then tallied and parents are grouped into authoritative, authoritarian or permissive parenting. It turned out that there are 9 permissive parents, 7 authoritative and 6 authoritarian parents. We want to test whether the average time a child can sit still is same in the three groups defined by maternal parenting style.

5.   Survival rate of American Burying Beetle (ABB) is observed for male and female beetles. If 8 of the 15 male beetles survived and 10 of the female burying beetles survived, can we test whether the female beetles have a significantly greater survival probability?   

6.   A new research explores the effect of anti-herpes drug to patients who were diagnosed with Alzheimer's disease (AD). 60 patients were recruited, 30 of which are treated with anti-herpes drug and the other 30 are placebo-controlled. The two groups are monitored every month for 12 months. Size of plasma Amyloid-β plaques, which are markers of AD, are measured at each time point. We are interested to test if there a significant difference in amyloid plaque size between the two study groups, on average?