1.A cereal manufacturer tests their equipment weekly to be assured that the proper amount of cereal is in each box of cereal. The company wants to see if the amount differs from the stated amount on the box. The stated amount on each box for this particular cereal is 12.5 ounces. The manufacturer takes a random sample of 100 boxes and finds that they average 12.2 ounces with a standard deviation of 3 ounces. Is this a one-tailed or two-tailed significance testing situation?

2.A researcher conducts a randomized experiment to test whether a diet that includes 100 grams of blueberries each day will improve the function of the cathelicidin antimicrobial peptide gene which is known to have an important role in the immune system. The gene's function is measured in 40 subjects who added 100 grams of blueberries to their daily diet and 40 control subjects who ate similar meals but without the blueberries. At the end of the experiment, a significance test is conducted and the p-value is found to be 0.0042. This says that...?

3.If the null hypothesis is true then it can not be rejected.

4.Use the following information for the five questions below. A researcher is interested in whether birth order has an effect on the size of a childs vocabulary. A vocabulary test is given to 100 children, all age five and all the oldest in their families. Later, the same vocabulary test is administered to the 100 next oldest sibling of these children when they reach five years of age (so both children in each family take the same test at age five). In this study, the oldest child scored higher on the vocabulary test for 63 of the 100 pairs of children (while the younger child scored higher for 37 of the pairs). A researcher wants to determine if this is strong evidence that order of birth has an effect on vocabulary size, or if these data can be explained by chance.

-What are the null and alternative hypotheses in this situation?

-What is the standard deviation of the proportion of times the older child scores higher if the null hypothesis is true? Explain how you got your answer.

-Is the normal approximation appropriate to use in this case? Explain briefly.

-What is the test statistic and the calculated p-value? Explain how you got your answer.

-What is the conclusion you should draw from these results?