1. Frame the null and alternative hypothesis (Step 1) for each of the following situations. Be sure to define any symbols you use.

a) A study claims that children first count to 10 successfully when they are 32 months old, on average. An early childhood education researcher believes that the innovative educational games available in the market may have brought that age down.

b) Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher.

c) We want to test whether the mean GPA for undergraduate students in American colleges is different from 2.5 (out of 4.0).

2. Suppose that a recent article by a historian stated that the mean time spent in jail by a first-time convicted burglar in the 20th century was 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years. Suppose that it is somehow known that the population standard deviation is 1.8 years. The hypotheses can then be framed as: H0 : = 2.5 vs. Ha : > 2.5

(a) Which of the following figures best describes the p-value for this hypothesis testing problem. Explain your reasoning. (numbers above red shaded area represent the corresponding probabilities).