You are the staff epidemiologist in a large school district of 100,000 pupils. Your school nurses have diagnosed a few kids with a sore throat of unknown etiology, thought to be a contagious infection. In the first week there was one new case (the first or ‘index’ case). In the second week (when the index case is still sick) there are new seven cases. What is the prevalence of this infection in the pupil population of your school district? What is the incidence? [i.e., most recently]

1.  A developmental psychologist would like to determine how much fine motor skill changes for children from age 3 to age 5. He takes a random sample of 9 three-year old children and gives each a manual dexterity test that measures fine motor skill. He tests these same children one and two years later, when they are each four- and five-years old. Higher scores on this test indicate better fine motor skills. Is there a significant difference in the motor skills at these ages? Test with an α = 0.01 and show ANOVA SPSS output.

In late July 2016, the Ohio Department of Health collected vials of water from 12 beaches on Lake Erie to investigate water quality. Those vials were being tested for E. coli bacteria which are found in human and animal feces and can cause illness and disease, should a swimmer accidentally ingest some water. These beaches had been found to be safe earlier in the summer with E. coli counts, on average of 88 per 100-millileter vial (about 3.4 ounces). However, E. coli counts can change due to weather and other variables. Experts consider it unsafe if a vial contains more than 88 E. coli bacteria. The mean E. coli count in the 12 vials was found to be 113.75 with a standard deviation of 93.9. Is this evidence that the water is unsafe? Test at the 1% level of significance. a) State the hypotheses.  b) Find the test statistic and p-value. c) Based on your p-value, state whether or not you will reject the null hypothesis and a statement of your findings, relating back to the problem.

It is known that 9 out of 10 people are right handed. Would 35 right handed people out of group of 93 be considered significantly low, significantly high, or neither? Show your work below.

Use the following scenario to answer the next 6 questions: M&Ms are your favorite vending machine snack and you purchase them often.  Lately, it seems like the bags have been having a disproportionate distribution of the colors.  The company claims that 24% of the candies per bag should be blue.  You decide to test this claim for yourself.  You purchase a large bag and find that 38 of the 224 candies are blue.  Before complaining to the company, you want to be fairly sure of your accusation, so you set a 1% significance level for your test.  Do you have sufficient evidence that the color distribution is different than advertised? Based on the data, the value of the test statistic is:

Imagine you work for a large company that sells a variety of cleaning supplies deigned to prevent the spread of viruses. You decide to investigate what the best method for preventing the spread of viruses is, if only one method is used. You design experiments with the following groups: hand sanitizer only, hand washing without soap, hand washing with soap, along with a control group. Each group has 181 observations during testing, beginning with a certain amount of the viruses present before treatment is applied. The amount of germs is being measured. You find a sum of squares between treatments of 578.59, along with a sum of squares error of 5022.05. Using this information, what is the F-statistic of your analysis?