Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495495 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490490 and 500500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490490 and 500500 ? (Enter your answer rounded to four decimal places.)

probability:

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ? of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.410.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 510 .

In answering the questions, use ?‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 505 and 515? (Enter your answer rounded to four decimal places.)

Probability - ?

(b) You sample 2525 students. What is the standard deviation of the sampling distribution of their average score ?¯  ? (Enter your answer rounded to two decimal places.)

Standard Deviation - ?

(c) What is the probability that the mean score of your sample is between 505505 and 515515 ? (Enter your answer rounded to four decimal places.)

Probability - ?

Some studies have shown that in the United States, men spend more than women on Valentine's Day. A researcher wants to estimate how much more men spend by observing the amounts spent for random samples of men and women. We want to estimate the difference (µ _men - µ _women) using a 90% confidence interval.

a) Find the AD (Anderson-Darling) for both Men and Women (using Minitab). (round to 3 decimal places)

b) Report the endpoints of the 90% confidence interval below. (Round to 1 decimal place)

MNO, Inc., a publicly traded manufacturing firm in the United States, has provided the following financial information in its application for a loan. The market value of equity is 1.58 times the book value of debt. Retained earnings are 5.27% of total assets. Sales are 52% of total assets. Earnings before interest and taxes are 32.87% of total assets. Finally, Working capital is 34.25% of total assets.

a) What is the Altman discriminant function value for MNO, Inc.?

b) Should you approve MNO, Inc.'s application to your bank for a $5,000,000 capital expansion loan?

c) If sales for MNO were 38% of total assets and the market value of equity was only half of book value, would your credit decision change?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.410.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500500 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 495495 and 505505 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 2525 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 495495 and 505505 ? (Enter your answer rounded to four decimal places.)

probability:

High school graduates: Approximately 78% of freshmen entering public high schools in the United States in 2005 graduated with their class in 2009. A random sample of 128 freshmen is chosen.

(a)Find the mean μp

.(b)Find the standard deviation σp

.

(c)Find the probability that less than 91% of freshmen in the sample graduated.

(d)Find the probability that between 68%and 83% of freshmen in the sample graduated.

(e)Find the probability that more than 68%of freshmen in the sample graduated.Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

High school graduates: Approximately

78%

of freshmen entering public high schools in the United States in

2005

graduated with their class in

2009

. A random sample of

128

freshmen is chosen. Use

(a)Find the mean

μp

.(b)Find the standard deviation

σp

.

(c)Find the probability that less than

91%

of freshmen in the sample graduated.

(d)Find the probability that between

68%

and

83%

of freshmen in the sample graduated.

(e)Find the probability that more than

68%

of freshmen in the sample graduated.

Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

High school graduates: Approximately

74%

of freshmen entering public high schools in the United States in

2005

graduated with their class in

2009

. A random sample of

175

freshmen is chosen. Use Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

(a)Find the mean

μp

.

Part 2 of 6

(b)Find the standard deviation

σp

.

Part 3 of 6

(c)Find the probability that less than

75%

of freshmen in the sample graduated.

Part 4 of 6

(d)Find the probability that between

64%

and

78%

of freshmen in the sample graduated.

Part 5 of 6

(e)Find the probability that more than

64%

of freshmen in the sample graduated.

Part 6 of 6

(f)Would it be unusual if the sample proportion of freshmen in the sample graduated was more than

83%

?

In 1974, the United States instituted a national speed limit of 55 miles per hour (mph), a move that generated a great deal of controversy. Proponents of the lower speed limit managed to avoid repeal of this national speed limit by effectively arguing that driving at 55 mph significantly reduced the number of traffic fatalities on U.S. highways. The argument was based on the fact that the total number of traffic fatalities dropped from 55,511 in 1973 to only 46,402 in 1974. Because people have questioned the validity of this argument, you are going to examine more rigorously the hypothesis that the reduction in fatalities was due to the institution of the 55 mph speed limit.

Procedure. Since the change to a 55 mph speed limit occurred a number of years ago, you must use archival data in your study. The U. S. government routinely makes available a wide variety of data on the U.S. population. Most public and private libraries either own or would be able to get the national or state statistics you need. Here is the data you would obtain for the present research question:

Table 1: Annual Traffic Fatalities on U.S. Highways

Year Number of fatalities

1966 53,041

1967 52,924

1968 55,200

1969 55,791

1970 54,633

1971 52,660

1972 56,278

1973 55,511

1974 46,402

1975 45,853

1976 47,038

1977 49,510

1978 50,226

Source: U.S. National Center for Health Statistics, Vital Statistics of the United States, annual.

One process of policy implementation decision is the rational comprehensive decision making process. Optimum decisions are the goal. While most of the literature and focus is on economic analysis of optimality, we also need to consider social optimality. Part of that process is through empirical analysis of data and determining its validity. Our knowledge of research designs can be a valuable tool. The purpose of this case analysis is to use those tools.

The hypothesis for this policy implementation analysis is the reduction in fatalities was due to the institution of the 55 mph speed limit. Using about 1000 words (three pages of discussion) and at least 3 scholarly references (one can be the text), review this case and respond to the questions:

What kind of threats to internal validity do these events represent?
Is this policy effective? Does the increasing number of fatalities after 1974 have any implications for the effectiveness of the speed limit intervention?
What is/are one or more of the rival explanations?
What would be at least one social cost of this policy? How is it defined and measured?
What decision making theory was used? What theory should have been used?
As a final paragraph, conclude how this case discussion can assist public administrator's decision making in their role as implementing policy.