1. A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally a random sample of 2000 registered voters in the southern half of the state is selected of which 900 support the candidate. A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is?

2. North Carolina State University looked at the factors that affect the success of students in a required chemical engineering course. Students must get a C or better in the course to continue as chemical engineering majors, so a "success" is a grade of C or better. There were 65 studemts from urban or suburban backgrounds (population 1), and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds (population 2), 30 of these students succeeded in the course. Estimate the difference between the success rates for all urban/surburban and rural/small-town students who plan to study chemical engineering at North Carolina State University with a 90% confidence interval

3. In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999?
In an hypothesis test to answer this question the test statistic is?

4. North Carolina State University looked at the factors that affect the success of students in a required chemical engineering course. Students must get a C or better in the course to continue as chemical engineering majors, so a "success" is a grade of C or better. There were 65 studemts from urban or suburban backgrounds, and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds, 30 of these students succeeded in the course. Is there good evidence that the proportion of students who succeed is different for urban/suburban students versus rural/small-town students? To test this hypothesis, what is the pooled sample proportion for these students?

5. A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Addititionally, a random sample of 2000 registered voters from the southern half of the state is selected of which 900 support the candidate. The sampling distribution for the difference in the sample proportions has standard error of what?

6. In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1999. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999?

7. In an experiment to learn if substance M can help restore memory, the brains of 20 rats were treated to damage their memories. The rats were trained to run a maze. After a day, 10 rats were given M and 7 of them succeeded in the maze; only 2 of the 10 control rats were successful. The z test for "no difference" against "a higher proportion of the M group succeeds"

may be inaccurate because the populations are too small.

may be inaccurate because some counts of successes and failures are too small.

is reasonably accurate because the conditions for inference are met.

has z = 2.6 and a P-value less than 0.005.

8. In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1999. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999? To determine this, you test the hypotheses