Twenty five high school students complete a preparation program for taking the SAT test. Here are the SAT scores from the 25 students who completed the SAT prep program: 434 694 457 534 720 400 484 478 610 641 425 636 454 514 563 370 499 640 501 625 612 471 598 509 531 The mean of these scores is 536.00. We know that the population average for SAT scores is 500 with a standard deviation of 100. The question is, are these students’ SAT scores significantly greater than a population mean of 500 with a population standard deviation of 100 ? Note that the the maker of the SAT prep program claims that it will increase (and not decrease) your SAT score. So, you would be justified in conducting a one-directional test. (alpha = .05).

Choose between

A - The prep program didn't result in significant improvement in SAT scores

B- The prep program resulted in significant improvement in SAT scores

An education minister would like to know whether students at Gedrassi high school on average perform better at English or at Mathematics. Denoting by μ1 the mean score for all Gedrassi students in a standardized English exam and μ2 the mean score for all Gedrassi students in a standardized Mathematics exam, the minister would like to get a 95% confidence interval estimate for the difference between the means: μ1 - μ2.

A study was conducted where many students were given a standardized English exam and a standardized Mathematics exam and their pairs of scores were recorded. Unfortunately, most of the data has been misplaced and the minister only has access to scores for 4 students.

The populations of test scores are assumed to be normally distributed. The minister decides to construct the confidence interval with these 4 pairs of data points. This Student's t distribution table may assist you in answering the following questions.

a)Calculate the lower bound for the confidence interval. Give your answer to 3 decimal places.

Lower bound =

b)Calculate the upper bound for the confidence interval. Give your answer to 3 decimal places.

Upper bound =

An assistant claims that there is no difference between the average English score and the average Math score for a student at Gedrassi high school.

c)Based on the confidence interval the minister constructs, the claim by the assistant can or cannot be ruled out.

A large school district claims that 80% of the children are from low-income families. 130 children from the district are chosen to participate in a community project. Of the 130 only 72% are from low-income families. The children were supposed to be randomly selected. Do you think they really were?

a. The null hypothesis is that the children were randomly chosen. This translates into drawing times

at random
with replacement
without replacement

from a null box that contains

b.
130 tickets, 72% marked "1" and 28% marked "0"
Thousands of tickets, 80% marked "1" and 20% marked "0"
Thousands of tickets marked either "1" or "0", but the exact percentages of each are unknown and estimated from our sample.
5 tickets, 1 marked "1" and 4 marked "0"

c. What is the expected value of the percent of 1's in the draws? (Don't type in the % sign)

%

d. What is the SD of the null box? (Note: We don't have to estimate the SD of the box from the sample SD because we can compute it directly from the percent of 1's in the null box. This is why we never use a t-test for problems that can be translated into 0-1 boxes.)

e. What is the standard error of the % of 1's in the draws? (Round to 2 decimal places.) %

f. What is the value of the test statistic z? (Round answer to 2 decimal places.)

g. What is the p-value? Click here to view the normal table
%

h. What do you conclude?
There is very strong evidence to reject the null, and conclude that the children were not randomly chosen.
We cannot reject the null, it's plausible the children were randomly chosen.

At a Midwestern business school, historical data indicates that 70% of admitted MBA students ultimately join the business school’s MBA program. In a certain year, the MBA program at the University admitted 200 students.

a. Find the probability that at least 150 students ultimately join the MBA program.

b. Find the probability that no less than 135 and no more than 160 students finally join the MBA program.

c. How many students should the MBA program expect to join the program?

d. What is the standard deviation of the number of students who will join the MBA program? e. Let X be the number of students out of 200 who will join the program. Would the empirical rule apply to the probability distribution of X in this case?

think of somebody who has authority over you, either at work, school or in another organization to which you belong( you can reference a family member). which do you and others most often overlook when trying to manage up? why? how could this approach to managing up be improved? are any steps missing? explain? manage up table: prepare your message, plan your delivery and tactics, deliver, follow up.

The University of Pittsburgh Medical (UPMS) School grades each class in the following manner:

All students whose score is plus or minus two standard deviations from the mean course score receive a grade of “Pass.”

Students whose score is above two standard deviations from the course mean receive a grade of “Pass with Distinction.”

And, students whose score is below two standard deviations from the course mean receive a grade of “Fail.” Course scores are always assumed to be normally distributed.

Approximately what percentage of medical students in each class receives a “Pass with Distinction”?

Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 48% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.

(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)
P(n) =  

(b) What is the probability that Bob first passes the bar exam on the second try (n = 2)? (Use 3 decimal places.)


(c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.)


(d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.)


(e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass? Hint: Use μ for the geometric distribution and round.

suppose that you encounter two traffic lights on your commute to school. Based on past experience, you judge that the probability is .60 that the first light will be red when you get to it, .50 that the second light will be red, and .40 that both lights will be red.

a)Determine the conditional probability that the second light will be red, given that the first light is red. (Here and throughout, show the details of your calculations.)

b)Are the events {first light is red} and {second light is red} independent? Justify your answer.

c) Given that at least one light is red, what is the probability that both lights are red? (Show your work.)

Unemployment among high school graduates is quite high due to a recession. City Community College is considering a new program to help young people get the training they need to be more employable. The college has collaborated with the municipal hospital to build a nurse’s aide program, a 1-year program that would lead to immediate employment. Initial financial analysis indicates that the total fixed cost of the program will be $200,000, which includes the cost of a 1-year rental of the facilities plus utilities, insurance, and administrative costs. The variable cost and step cost together are $10,000 per student, which pays for faculty salary, student lunches, and teaching materials and textbooks. The state kicks in $5,000 per student, and the tuition based on market analysis is $6,000. Given that the nurse’s aide program has never been offered in the region before and will be under financial pressure due to current funding cuts, the college’s board of trustees would like to know how many students would need to be enrolled for the program to break even. The board also wants to know what other options it will have to mitigate these financial issues if the expected enrollment is below the break even point, given the high profile of the program at a time when employment and economic recovery are critical.Consider two possibilities: (1) Funding is limited to $100,000, or (2) with the benefit of efficiencies, variable and step costs can be reduced to $9,500. You are required to do a financial analysis of the proposed program. Please provide a spreadsheet solution and a written explanation of your approach.