1. According to the National Center for Education Statistics, 50.5% of students enrolled in a U.S. higher education program during 2011-12 attended school full-time. It is believe that the current percentage of students enrolled in a U.S. higher education program that attend school full-time is lower than the percentage reported by NCES. To test this claim, a random sample of 643 of college students is selected.

2. True or False. For each statement below, determine whether it is true or false. a. It is believed that the average number of students enrolled in an online course at NKU is more than 15 students. A hypothesis test for the population proportion can be used to test this claim b. The following statement is always true regarding the probability of a hypothesis test: 0 probability 1 3. According to a recent New York times article, Democrats make up 51% of early voters nationally in the 2022 midterm elections (as of October 20). It is believed that the actual percentage of early voters that are Democrats will be different than this. A random sample of 488 early voters is selected. Suppose 232 of the sampled early voters were Democrats. a. What is the variable involved in this scenario? Classify this variable as categorical or quantitative.

b. Use this sample to conduct the appropriate hypothesis test using a significance level of 0.01.

c. Based on your decision made in part b, what type of error is possible? Type I error Type II error no error possible

d. Describe the error you selected in part c in the context of this problem by choosing one correct option for each of the two parts shown. The data leads us to support/not support (choose 1) the claim that the percentage of early voters that are Democrats is different than 51%, when in reality the percentage is/is not (choose 1) different than 51%.