How fast can male college students run a mile? There’s lots of variation, of course. During World War II, physical training was required for male students in many colleges, as preparation for military service. That provided an opportunity to collect data on physical performance on a large scale. A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.01 minutes and standard deviation 0.7 minute.

It's good practice to draw a Normal curve on which this mean and standard deviation are correctly located. To do this, draw an unlabeled Normal curve, locate the points where the curvature changes (this is 1 standard deviation from the mean), then add number labels on the horizontal axis.

Use the Empirical Rule to answer the following questions.

1. What range of times covers the middle 99.7% of this distribution?
   
   From ______to _____minutes Round to 2 places.
   
2. What percent of these runners run the mile between 5.61 and 9.11 minutes?
   
   ______% Round to 2 places.
   
3. What percentage of the these running times are faster than 7.71 minutes?
   
   ________% Round to 2 places.

1. The average expenditure per student for a certain school year was $10337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10798. At α =0.01 level of significance, can it be concluded that the average expenditure has changed?

2. (10 pts) Suppose when you were visiting universities and deciding which to attend, the admission officers at Tennessee Wesleyan(TW) claimed TW students graduate in 4.25 years or less. You are now a student at TW and notice that a lot of students are graduating in more than 4.25 years. Therefore, you doubt that you were given accurate graduation rates by the TW admission officers. You collect data and compute graduation rates of TW graduates from the last 10 years (n=10). You obtain a mean graduation rate of 4.74 years and a standard deviation of 0.76 years. Do you have strong enough evidence to prove that TW admissions officers are not providing accurate rates at α =0.05 level of significance? Use hypothesis testing to determine your conclusion.

2-

The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

-A two-sided test with zcrit = -1.645 and 1.645.

-n 1 = n 1999 = 334

-n 2 = n 2009 = 843

-p ^ 1 = p ^ b i n g e 1999 = 0.422

-p ^ 2 = p ^ b i n g e 2009 = 0.212

A) Calculate the appropriate test statistic showing your work. What is the standard error?

B) What is the test statistic value?

C) Calculate the corresponding p-value from the appropriate table.

D) Construct a 90% confidence interval around the difference-in-proportions estimate. Lower bound and upper bound values?

For each exercise, answer the following along with any additional questions. Assume group variances are equal (unless the problem is ran via statistical software). |  Provide the null and alternative hypotheses in formal and plain language for appropriate two-tailed test (viz., dependent or independent) at the 0.05 significance level  Do the math and reject/accept null at a=.05. State your critical t value.  Explain the results in plain language.  Calculate the 95% confidence interval for the difference in means and state both formally and in plain language if appropriate.|

1. The State of Florida severely cut funding for the TRUTH campaign (advertising which is aimed at teenagers to reduce smoking). Advocates claim that TRUTH reduces teen smoking. To demonstrate this, they provide two separate samples of the state’s high school students reporting their number of cigarettes smoked per day two years before (nine students) and two years after the start of TRUTH (eight students). (C11PROB1.SAV) Before TRUTH: 5, 5, 8, 0, 0, 10, 0, 4, 10 After TRUTH: 6, 0, 6, 7, 0, 0, 2, 5

The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

-A two-sided test with zcrit = -1.645 and 1.645.

-n 1 = n 1999 = 334

-n 2 = n 2009 = 843

-p ^ 1 = p ^ b i n g e 1999 = 0.422

-p ^ 2 = p ^ b i n g e 2009 = 0.212

A) Calculate the appropriate test statistic showing your work. What is the standard error?

B) What is the test statistic value?

C) Calculate the corresponding p-value from the appropriate table.

D) Construct a 90% confidence interval around the difference-in-proportions estimate. Lower bound and upper bound values?

Question #5: Educational psychologists were interested in the impact the "Just Say No!" Program and contracts on drunk driving among males vs. female teenagers. With the cooperation of school officials, 16-year-old students were matched and randomly assigned to one of two groups, with equal numbers of males and females in each group. Group A participated in a "Just Say No!" program, which required a one-hour information session instead of P.E. for six weeks. Students were presented with written factual information, motivational lectures, guidance films, and assertiveness training. Students were also encouraged to sign a personal responsibility contract that stipulated that they would not drink and drive. Group B participated in regular P. E. classes for the six-week experimental period. Please answer the following questions and justify your answer.

(a) Identify the experimental design.

(b) What is the independent variable? Quasi-independent variable? What is the dependent variable?

(c) Diagram this experimental design.

(d) State at least one potential confounding variable?

(e) How many main effects, interaction effects, simple main effects of A, and simple main effects of B are there?

Whereas grading students’ homework is an important aspect of a professor’s job, reviewing homework solutions is an important ingredient in the learning process for a student. Research indicates that the longer it takes a professor to grade a homework the less likely that a student will review the homework solutions, when made available. In the past, in Professor Johnson PHYS 500 class, nonadherence on part of a few students to a prescribed HW submission format has often delayed the turnaround time for posting homework grades. In fact, in a few cases, homework’s were left ungraded till the end of the semester. Concerned about the impact this would have on student learning, the professor regularly reminded the students about the submission format, which yielded marginal positive results. Note that the time taken by the professor to grade a student's homework is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes.

1. What is the probability that a randomly selected homework will require less than 16 minutes to grade?
2. What is the probability that randomly selected homework will require more than 12 minutes to grade?
3. What is the probability that randomly selected homework will require between 11 and 15 minutes to grade?

Part A: Imagine a researcher thinks that using caffeine before a test increases test scores. If they had the consent of all the students in a 120-person class to participate in a study, a good experimental design would follow which protocol?

Part B: In a regression equation, the coefficient for the constant (aka intercept) represents,

CVP-Sensitivity analysis; spreadsheet recommended. Quality Cabinet construction is considering introducing a new cabinet-production seminar with the following price and cost characteristics.

Tution…………………………………………… $200 per Student
Variable Costs (wood, supplies, etc..)……………………. $120 per Student
Fixed Costs (advertising, instructor’s safety, insurance, etc.)………………….. $400.00 per year.

What enrollment enables Quality Cabinet construction to break even?

b. How many students will enable Quality Cabinet construction to make an operating profit of $200,000 for the year?

c. Assume that the projected enrollment for the year is 8,000 students for each of the following situations:

1. What will be the operating profit for 8,000 students?

2. What would be the operating profit if the tuition per student (that is,l sales price) decreased by 10 percent? Increased by 20 percent?

3. What should be the operating profit if variable costs per student decreased by 10 percent? Increased by 20 percent?

4. Suppose that fixed costs for the year are 10 percent lower than projected whereas variable costs per student are 10 percent higher than projected. What would be the operating profit for the year?

The owner of a small company asked a CPA to conduct an audit of the company's records. The owner of the company told the CPA that the audit was to be completed in time to submit audited financial statements to a bank as part of a loan application. The CPA immediately accepted the engagement and agreed to provide an auditor's report within three weeks. The owner agreed to pay the CPA a fixed fee plus a bonus if the load was granted. The CPA hired two accounting students to conduct the audit and spent several hours telling them exactly what to do. The CPA told the students not to spend time reviewing the internal controls but instead to concentrate on proving the mathematical accuracy of the ledger accounts and summarizing the data in the accounting records that supported the company's financial statements. The students followed the CPA's instructions and after two weeks gave the CPA the financial statements which did not include any footnotes. The CPA reviewed the statements and prepared an unmodified auditor's report. The report did not refer to GAAP or to the consistent application of GAAP. Briefly describe at least three principles underlying AICPA auditing standards and indicate how the actions of the CPA resulted in a failure to comply with each principle.