A student conducts a simple random sample of students from her high school and finds that 21 out of 100 students in her sample regularly walk to school. Give a point estimate for the proportion of all students at her high school who regularly walk to school. For each combination of sample size and sample proportion, find the approximate margin of error for the 95% confidence level. (Round the answers to three decimal places.) In a sample of 16 students, 15 were right-handed. Can we construct a 95% confidence interval for the proportion of all students who are right-handed? A study reported that 49% of Internet users have searched for information about themselves online. The 49% figure was based on a random sample of Internet users. Suppose that the sample size was n = 400. In a randomly selected sample of 400 registered voters in a community, 260 individuals say that they plan to vote for Candidate Y in the upcoming election. A certain set of plants were constantly dying in the dry environment that was provided. The plants were moved to a more humid environment where life would improve.

2. Recent data from graduates of KU School of Medicine in the past two years found that the mean starting salary for the 104 female physicians in their sample was $224,426.12 with a standard deviation of $27,792.73. For the 90 male physicians, the mean starting salary was $235,044.12 with a standard deviation of $33,509.25.

1. a) Is this sufficient evidence at alpha=.01 that among graduates of KU School of Medicine in the past two years the mean starting salary for men is higher than the mean starting salary for women? (10 points)

2. b) Is this sufficient evidence at alpha=.05 that among graduates of KU School of Medicine in the past two years the mean starting salary for men is higher than the mean starting salary for women? Explain.**You do not need to repeat all 5 steps for this part, just explain how you came to your conclusion (1 point)

3. c) Calculate and interpret a 96% confidence interval for the mean starting salaries of female physicians who graduated from KU School of Medicine. (6 points)

4. d) What is the margin of error for the interval that you calculated is part c? (2 points)

8.) What percent of the adolescents who were not in school had a desired pregnancy?

9.) What percent of the adolescents who were in school full time had a desired pregnancy?

10.) The study reports that the Chi-square test between pregnancy desire and being in school is significant. Interpret these results along with the answers you gave to questions 8 and 9 to draw a conclusion.

Variable Desired Pregnancy [n 92; n (%)] Undesired Pregnancy [n 119; n (%)] OR (95% CI) Adjusted OR (95% CI)

Hispanic 37 (40.2) 23 (19.3) 2.98 (1.59–5.59) 2.54 (1.33–4.87) W

White 8 (8.7) 9 (7.6) 1.65 (0.60–4.55) 1.34 (0.47–3.83)

African American 47 (51.1) 87 (73.1) Reference group Reference group

Part-time student 1 (1.1) 4 (3.4) 0.45 (0.05–4.13) 0.46 (0.05–4.36)

Not in school 42 (45.7) 27 (22.7) 2.80 (1.54–5.07) 2.42 (1.31–4.48)

Full-time student 49 (53.3) 88 (73.9) Reference group Reference group

When discussing SAT mathematics scores for high school students in Texas, an educator states that the scores overestimate the math ability of high school seniors because only a select minority of students actually take the test. The educator believes that the mean score would be 495 if all high school seniors took the test. You believe the average would be higher and wish to test this claim using a hypothesis test.

You conduct a simple random sample of 100 high school seniors and find the mean score of the sample is 511. From previous studies of SAT scores, you believe the population standard deviation is σ=81.

1. At the α=0.01 level, test your claim that the mean score of seniors is higher than 495.
   1. (2 pts.) Give the null and alternate hypotheses for this problem.

2. (2 pts.) Find the critical value for this problem and sketch the critical region.

3. (2 pts.) Calculate the test statistic for this problem.

4. (2 pts.) Make your decision about the null hypothesis and summarize your results.

2. (2 pts.) If the significance level was α=0.05 , would this change your conclusion? Why or why not?

You are deciding if you should go to Law School, which is a three year degree. If you do not go to law school, you will earn $47,000 per year. While you are in law school, you will have the opportunity to take a part-time job working for a professor for $12,000 per year. Tuition is $30,000 per year. Once you get a law degree, you will earn $100,000 per year. For simplicity, assume no raises. a) Suppose the interest rate is 5% and you are considering a 10 year horizon (either you work for 10 years with no law degree, or you get your law degree and then work for an additional 7 years). Should you go to law school? Show all your work. (I encourage you to do this in excel, in which case you may print out and attach your spreadsheet. Make sure it is formatted so the print-out is easy to read and interpret.) b) Is the law degree more or less worth it as the return to education decreases? c) Is the law degree more or less worth it as the interest rate increases?

Mrs. Inwood teaches a 7^th grade mathematics class who is interested in how many hours of homework a typical student from their middle school does in a week. The middle school contains grades 6-8 and has 275 students in total. Her students brainstormed plans on how to select a sample of students to survey. Listed below are several of the plans.

Provide a thorough analysis of the appropriateness (advantages and/or disadvantages) of each suggested sampling plan.

1.     Survey every fourth student (Student #4, Student #8, etc.) on each homeroom class list.

2.     Since there are 275 students in the middle school, put 250 white chips and 25 blue chips in a box. As students enter the cafeteria for lunch, have each one take a chip from the box. Survey the 25 students who get a blue chip.

3.     Have each student in Mrs. Inwood’s class conduct the survey in his or her history class.

4.     Distribute surveys to students as they enter the middle school building in the morning and ask students to return their completed surveys to the office at the end of the day.

The following data are from the Bureau of Labor Statistics and shows the outcome of women at age 46:

Less than High school

High school grad

Some college

Bachelor’s degree +

Ever Married

0.09

0.30

0.23

0.24

Ever Divorced

0.05

0.15

0.11

0.07

Never Married

0.02

0.05

0.03

0.04

Note that ever married and ever divorced are not mutually exclusive—the ”ever divorced” category is a subset

of the ”ever married” category.

(a) What percent of women were ever married?

(b) What percent of women have a bachelor’s degree or higher?

(c) If a woman has been divorced, what’s the probability that she has less than a high school diploma or is a

high school graduate with no college?

(d) My sister is getting married this summer. According to this data, what’s the unconditional probability she

gets divorced? (i.e. what’s the probability she gets divorced if we don’t factor in her education level?)

(e) What’s the probability my sister gets divorced given she has a Bachelor’s degree?

(f) Is divorce rate independent of education level?

(Question 6) To test whether students in a higher grade level will be less disruptive in class, a school psychologist records the number of documented interruptions during one day of classes from nine local high schools. The sample consisted of nine (n = 9) freshman, sophomore, junior, and senior high school classes. The data for each high school class are given in the table.

(a) Complete the F-table. (Round your answers to two decimal places.)

(b) Is it necessary to compute a post hoc test? Explain. (Assume alpha equal to 0.05.)

Yes, post hoc analyses are appropriate because the ANOVA is significant.

No, post hoc analyses are not appropriate because the ANOVA is not significant.   

The article "College Graduates Break Even by Age 33" reported that 5.7% of high school graduates were unemployed in 2008 and 9.7% of high school graduates were unemployed in 2009.† Suppose that the reported percentages were based on independently selected representative samples of 300 high school graduates in each of these two years.

(a)Construct a 99% confidence interval for the difference in the proportion of high school graduates who were unemployed in these two years. (Use p2008 − p2009. Round your answers to three decimal places.)

B) The same article reported that 2.6% of college graduates were unemployed in 2008 and 4.6% of college graduates were unemployed in 2009. Suppose that the reported percentages were based on independently selected representative samples of 500 college graduates in each of these two years. A 95% confidence interval for the difference in the proportion of college graduates who were unemployed in these two years was calculated to be (−0.043, 0.003). Is the confidence interval from part (a) wider or narrower than this confidence interval? (Round your answers to three decimal places.)The width of the confidence interval in part (a) is _______ and the width of the given confidence interval is _________ . Thus, the confidence interval in part (a) is

Your parents have accumulated a $170,000 nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Courtney. However, Courtney has decided to forgo college and start a nail salon. Your parents are giving Courtney $32,000 to help her get started, and they have decided to take year-end vacations costing $10,000 per year for the next four years. Use 8 percent as the appropriate interest rate throughout this problem. Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

a. How much money will your parents have at the end of four years to help you with graduate school, which you will start then? (Round your final answer to 2 decimal places.)

Funds available for graduate school?

b. You plan to work on a master’s and perhaps a PhD. If graduate school costs $29,780 per year, approximately how long will you be able to stay in school based on these funds? (Round your final answer to 2 decimal places.)

Number of years?