1. 1. (4 points) The following is a subset of the data published by U.S. News & World Report in 1995. The data specify the graduation rate of 5 different U.S. colleges and the instructional expenditure per student at each of the colleges. Use the data to answer the following questions.

Table: Graduation Rate and Expenditure per Student

1. Generate the regression equation for predicting graduation rates from the expenditure per student.
2. Using the regression equation, predict the graduation rate for a school that spends $ 6,700 per student.
3. Use the regression equation to determine how much a school would need to spend to obtain a 100% graduation rate.

2. The average score on the math section for all women taking the SAT in 1972 was 489 , and the average score on the math section for all women taking the SAT in 2006 was 502. Assume that in both years the standard deviation was 100.

1. If a woman had taken the math SAT in 1972 and earned a score of 560 , what would her \(z\) score be?
2. If a woman had taken the math SAT in 2006 and earned a score of 560 , what would her \(z\) score be?

3. (3 points) Centers for Disease Control data from 1999-2002 indicate that the average height for U.S. women aged 20 to 74 is 64 inches with a standard deviation of 2 inches. Assume you are interested in whether the heights of women who attend your university are similar to those of the general population. You randomly sample 50 women from your university and find that their average height is 63.7 inches.

1. Based on these data, what is the standard error for the sampling distribution of the mean of women's heights?
2. Calculate the \(z\) statistic for the sample of women from your university.
3. In approximately what percentile is the sample from your university?

4. ( 3 points) Cromley and Azevedo (2007) were interested in the reading comprehension performance of ninth graders. Students' reading comprehension was assessed with a test in which population mean performance is 33 , with a standard deviation of 10 .

1. One of the researchers' goals was to identify the bottom \(30 \%\) of students, so they could determine the characteristics of students who struggled with reading. What cutoff score would Cromley and Azevedo use to identify the bottom \(30 \%\) of readers?
2. Let's say we wanted to identify the best \(10 \%\) of readers to put into an advanced class. What cutoff score on the reading comprehension test would we use?

5. (6 points) The average age for licensed drivers in a county is \(\mu=42.6, \sigma=12\), and the distribution is approximately normal. A county police officer was interested in whether the average age of those receiving parking tickets differed from that of the average age of the population. She obtained a sample of \(N=25\) drivers receiving parking tickets. The average age for these drivers was \(M=40.5\). Perform the six steps of hypothesis testing (not including assumptions) necessary to determine whether this group differs from the population of drivers in the county.

6. (6 points) In a fictional study, a pretest-posttest design was used to examine the influence of a television program on children's aggressiveness. The number of aggressive responses was measured during an observation period both before and after the television program. Perform the six steps of hypothesis testing (not including assumptions) using the following data to determine if there is a difference in the number of aggressive behaviors in children after having viewed the television program.

Table: TV and Aggressiveness

7. (6 points) A researcher is interested in whether herbal remedies are effective in relieving allergies, and if so, which ones are most effective. The researcher takes a group of 20 allergy sufferers and randomly assigns each one to receive either herbal tea, a homeopathic administration of allergens, a traditional antihistamine, or a placebo pill. The dependent measure is the number of allergy complaints by patients during weeks 2-3 of the treatments. Perform the six steps of hypothesis testing (not including assumptions) on the following set of fictional data.

Table: Herbal Remedies

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