In the description of the following experiment, determine the experimental factor. During a study testing a new vaccine for Zika virus, the research team grouped the volunteers enrolled for the test into Group A and Group B. Group A received an inert drug (placebo) while Group B received the vaccine.

Select the correct answer below:

whether or not a person contracts the Zika virus

the effectiveness of the new vaccine

the drug received by each group

the group receiving the new vaccine

1. A population has a mean of 40 and a standard deviation of 10. Find the z-scores corresponding to each of the following raw scores:

1. 60.00

2. 32.46

2. A population has a mean of 3 and a standard deviation of 3. Turn the following z scores into raw scores:

1. Z score: 1.75

2. Z score: -2.35

3. For the z-scores below, find the percentile rank (percent of individuals scoring below):

1. 2

2. -0.5

4. First graders in the state of Virginia get an average score of 20 on a reading test (higher score reflect higher levels of performance). A teacher is using a new method to teach reading. She predicts that by the end of the first grade, students getting her new method will have significantly higher scores on reading than those in the population. The mean score of the 25 students in her class is 23.2 and the standard deviation of the population is 4.7.

1. State the null and alternative hypotheses.

2. Calculate the z-score.

This problem is also a Monte Carlo simulation, but this time in the continuous domain: must use the following fact: a circle inscribed in a unit square

has as radius of 0.5 and an area of ?∗(0.52)=?4.π∗(0.52)=π4.

Therefore, if you generate num_trials random points in the unit square, and count how many land inside the circle, you can calculate an approximation of ?

For this problem, you must create code in python

(B) Without drawing the diagram, calculate the value of ? you would get from 10⁵ trials.

(C) After completing (B), try to get a more accurate value for ? by increasing the number of trials.The results will depend on your machine

A simple random sample of size n=36 is obtained from a population with mean=89 and standard deviation = 6

​(c) What is P ( x overbar less than or equal to 86.65)​? ​

(d) What is P(88.5 < x overbar < 91.25)?

​(a) Describe the sampling distribution of x overbar.

​(b) What is P ( x overbar > 90.85 )?

1. A public health researcher wants to collect data about race of people who have HIV. His hypothesis is that HIV rates will affect African Americans differently than other races.

1. What would the null hypothesis be for this study?

2. What is the research hypothesis?

3. The researcher publishes an article saying that there were, in fact, more African Americans with HIV than other races with the disease in his study. Did the researcher fail to reject or reject the null hypothesis?

2. A medical researcher is testing if a migraine medication significantly reduces migraines.

1. What would a Type I error look like?

2. What would a Type II error be in this study?

PLEASE PROVIDE ANSWER FOR DEDICATED QUEUES:
Burger Dome sells hamburgers, cheeseburgers, French fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Suppose that Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 21 customers per hour and 1 customer processed per minute.

Compare a multiple-server waiting line system with a shared queue to a multiple-server waiting line system with a dedicated queue for each server. Suppose Burger Dome establishes two servers but arranges the restaurant layout so that an arriving customer must decide which server's queue to join. Assume that this system equally splits the customer arrivals so that each server sees half of the customers. How does this system compare with the two-server waiting line system with a shared queue? Compare the average number of customers waiting, average number of customers in the system, average waiting time, and average time in the system. If required, round your answers to four decimal places.

Comparing these numbers, it is clear that the shared or dedicated results in better process performance than the shared or dedicated?? .

Andi and Budi will meet. Suppose A is an event where Andi arrives late, and B is an event where Budi arrives late, with P (A) = 0.1 and P (B) = 0.3. What is the chance the two of them will meet on time if

a. Genesis A and B are independent (independent)?
b. P (B | A) = 0.5?
c. P (B | A) = 0.1?

Say we have the following hypotheses

H0: μ <50

HA: μ > 50

We know that the population standard deviation is 8. If we collect a sample of 64 observations and want α = 0.05, calculate whether or not we reject the null for the following sample means: a.x̅=52.5

b.x̅=51

c.x̅=51.8

For questions 1-5, X1, X2, ... , X23 is a random sample from a distribution with mean μ = -1.02 and variance σ2 = 0.62.

For questions 5-10, X1, X2, ... , X28 is a random sample from a distribution with mean μ = -8.77 and variance σ2 = 1.28.

1. Find μx, the mean of the sample average.
2. Find σ2x, the variance of the sample average.
3. Find P(X ≤ -1.14).
4. Find P(X > -1.14).
5. Find P(-1.08 < X ≤ -0.94).
6. Find μx, the mean of the sample average.
7. Find σ2x, the variance of the sample average.
8. Find P(X ≤ -8.47).
9. Find P(X > -8.47).
10.Find P(-9.02 < X ≤ -8.64).

Consider an experiment where you toss a coin as often as necessary to turn up one head.Suppose that the probability of having a tail is p(obviously probability of a head is 1−p).Assume independence between tosses.a) State the sample space.

b) Let X be the number of tosses needed to get one head. What is the support (possible values ofX)?

c) FindP(X= 1),P(X= 2) andP(X= 3).

d) Deduce the pmf of X from part c).

Suppose you have to calculate the number of popping sounds popcorn does in each five-second interval. For example:

Discuss what type of variables you have, such as quantitative or qualitative, discrete or continuous, nominal, ordinal, interval, or ratio.

There are two variables: 5 seconds interval and number of popping sounds. Please describe them. Thank you.

1. 1000 used car tires are being evaluated by a major insurance company. The quality of the tiers are based on the depth of the treads and years in use. The results from 1000 tires are summarized as the following:

Let A denote the event that a tire is new (less than 2 years old), and let B denote the tire has low depth for treads (less than 3 mm). Determine the number of castings in

1. Put in writing what A∩ B means.
2. Find A∩ B
3. Find A∪ B¢
4. What is the probability that a randomly selected tire is not new with high treads depth?
5. What is the probability that a randomly selected tire is not new with low treads depth?
6. If a selected tire was found to be new, find the probability that it is with high treads depth.
7. Find P(A | B)

Test the claim that the mean GPA of night students is smaller than 3.2 at the .025 significance level.

Based on a sample of 75 people, the sample mean GPA was 3.18 with a standard deviation of 0.06

The test statistic is (to 3 decimals)

The critical value is (to 3 decimals)

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”?

Grades on a standardized test are known to have a mean of 500 for students in the US. The test is administered to 600 randomly selected students in Florida. In this subsample, the mean is 508, and the standard deviation is 75

i. Construct a 95% confidence interval for the average test score for students in Florida.

ii. Is there statistically significant evidence that students in Florida perform differently from other students in the US?

iii. Another 500 students are selected at random from Florida. They are given a 3 hour preparation course before the test is administered. Their average test score is 514, with a standard deviation of 15. Construct a 95% confidence interval. Is there statistically significant evidence that the preparation course helped? What conditions must be met in order for the results to have a causal interpretation?