A researcher wishes to​ estimate, with 95​% ​confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 44​% of the true proportion.

​a) No preliminary estimate is available. Find the minimum sample size needed.

​b) Find the minimum sample size​ needed, using a prior study that found that

46​% of the respondents said they think their president can control the price of gasoline.

​c) Compare the results from parts​ (a) and​ (b).

Identify the Distribution

Select the Distribution that best fits the definition of the random variable X in each case.

Question 1) In a single game of (American) roulette, a small ball is rolled around a spinning wheel in such a way that it is equally likely to land in any of 38 bins. Sixteen of the bins are Red, another 16 are Black, and the remaining 2 are Green. Suppose 5 games of roulette are to be played. What is the joint distribution of the number of times the ball lands Red and the number of times the ball lands Green?

Question 2) Each hurricane independently has a certain probability of being classified as "serious." A climatologist wants to study the effects of the next 5 serious hurricanes. X = the number of non-serious hurricanes observed until the data is collected.

Question 3) The amount of anesthetic required to keep a person asleep during a 1-hour surgery is directly related to their weight. A hospital is performing 10 such surgeries on 10 independent patients. X = the total amount of anesthetic required.

Question 4) To measure the concentration of chemicals in rain, a square of absorbant paper is placed outside in a rainstorm for a few seconds, where raindrops are equally likely to land anywhere on it. X = the x-coordinate of a random raindrop on the paper.

Question 5) In Lotto 6/49 a player selects a set of six numbers (with no repeats) from the set {1, 2, ..., 49}. In the lottery draw, six numbers are selected at random. Let X = the first number drawn.

Question 6) Emails arrive at a server independently of each other at the uniform rate throughout the day with little chances of more than one email arriving at the same instant. X = time between two consecutive emails.

According to the website Rotten Tomatoes, the movie “The Peanuts Movie” received 92 critic reviews. Of these 92 reviews, 79 of them were positive reviews (a fresh tomato) and 13 of them were negative reviews (a rotten tomato.) Test the claim made by 20^th Century Fox, the company which made The Peanuts Movie that more than 80% of all critics gave this movie positive reviews. To this end find the following (at alpha = 0.05):

1. State the Null Hypothesis
2. State the Alternative Hypothesis
3. Find the test statistic
4. State the critical value
5. Make conclusions about your hypothesis test
6. Find the P-value for this sample data

Eastman Publishing Company is considering publishing an electronic textbook about spreadsheet applications for business. The fixed cost of manuscript preparation, textbook design, and web-site construction is estimated to be $160,000. Variable processing costs are estimated to be $6 per book. The publisher plans to sell single-user access to the book for $46.

a.) Build a spreadsheet model to calculate the profit/loss for a given demand. What profit can be anticipated with a demand of 3500 copies?

b.) Use a data table to vary demand from 1000 to 6000 in increments of 200 to assess the sensitivity of profit to demand.

c.) Use Goal Seek to determine the access price per copy that the publisher must charge to break even with a demand of 3500 copies.

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfill each week is 2. (a) What is the probability that in a given week the plant cannot fulfill all the placed orders? (b) Assume the answer to part (a) is 20%. Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

The amount of time part time worker at a pet store is normally distributed with a mean of 25 hours and a standard deviation of 2.5 hours. In a random sample of 25 employees, what is the probability that a worker will work for between 24 and 26 hours?

A student goes to the university library. The probability that the student checks out the science book for the science class is 0.40; the probability that the student checks out the math book is 0.30; and the probability that the student checks out both the science and math book is 0.20. What is the probability that the student checks out the science and the math book?

Dutch elm disease of American elm trees is caused by a fungus. It is known that 95% of elm trees in a city that have been treated with a fungicide recover from the disease. What is the probability that in a random sample of 4 elm trees in this city, at least 3 trees recover when treated with the fungicide?

A canning company claims that the amount of sugar in a cup of cherries is 13.2 grams. The population is normally distributed with a population standard deviation known to be 0.5 grams. The researcher took a sample of 25 cups of cherries and found a mean of 12.95 grams of sugar. Test at the 5% significance level that the amount of sugar in a cup of cherries is different than what the company claims. What is the p value for this test and what is your conclusion?

1. State the Null Hypothesis
2. State the Alternative Hypothesis
3. Find the test statistic
4. Find the critical value or values
5. State the conclusions to the hypothesis test.

Please find all of the above for the scenarios below

Part I. A university is looking into its mathematics placement procedure. The university assumes its population mean math SAT score of all incoming freshmen is 600. Suppose that a simple random sample of 33 freshmen at that university reveals a mean math SAT score of 614 with a standard deviation of 47. Test the claim, at the 0.05 alpha level, that the mean math SAT score of freshmen at this university is more than 600

Part II. Question 2: This same university is looking into its English placement as well. The university assumes its population mean Verbal SAT score for all incoming freshmen is 570. Suppose that a simple random sample of 51 freshmen at that university reveals a mean verbal SAT score of 520 with a standard deviation of 35. Test the claim, at the 0.05 alpha level, that the mean Verbal SAT score of freshmen at this university is different from 570.

Identify the Distribution

Select the Distribution that best fits the definition of the random variable X in each case.

Question 1) You have 5 cards in a pile, including one special card. You draw 3 cards one at a time without replacement. X = the number of non-special cards drawn.

Question 2) The number of car accidents at a particular intersection occur independently at a constant rate with no chance of two occurring at exactly the same time. X = the number of accidents on a Thursday.

Question 3) A soccer player has a certain probability p of being injured in each game, independently of other games. X = the number of games played before the player is injured.

Question 4) A jury of 12 people each independently vote on whether a defendant is guilty or not guilty, each with the same probability. X = the number who vote guilty.

Question 5) In a single game of (American) roulette, a small ball is rolled around a spinning wheel in such a way that it is equally likely to land in any of 38 bins. Sixteen of the bins are Red, another 16 are Black, and the remaining 2 are Green. Suppose 5 games of roulette are to be played. What is the joint distribution of the number of times the ball lands Red and the number of times the ball lands Green?

Question 6) Each hurricane independently has a certain probability of being classified as "serious." A climatologist wants to study the effects of the next 5 serious hurricanes. X = the number of non-serious hurricanes observed until the data is collected.

Question 7) The amount of anesthetic required to keep a person asleep during a 1-hour surgery is directly related to their weight. A hospital is performing 10 such surgeries on 10 independent patients. X = the total amount of anesthetic required.

Question 8) To measure the concentration of chemicals in rain, a square of absorbant paper is placed outside in a rainstorm for a few seconds, where raindrops are equally likely to land anywhere on it. X = the x-coordinate of a random raindrop on the paper.

Question 9) In Lotto 6/49 a player selects a set of six numbers (with no repeats) from the set {1, 2, ..., 49}. In the lottery draw, six numbers are selected at random. Let X = the first number drawn.

Question 10) Emails arrive at a server independently of each other at the uniform rate throughout the day with little chances of more than one email arriving at the same instant. X = time between two consecutive emails.

Hi there,

I want to make an experiment that you can use a one sample z- test and interval on it. The project is a paper helicopter and we can make as many we like and then explain the process It should be dropped from a height and a weight like paperclip in the bottom to make fall. Please help me with this project.

1st: what is inference procedure and the variables you are

estimating

2nd: the experiment procedure, the condition and how we can prevent bias

3rd. what kind of difficulties I could have on making such an experiment.

The mean age of Senators in the 109th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At \alpha α = 0.05, is there sufficient evidence that state senators are on average younger than the Senators in Washington? What is the statistic value? Round your answer to the nearest hundredths.

[20pts] In 2005, 45% of parents with children in high school felt it was serious problem that high school students were not being taught enough math and science. A recent survey found that 52 out of 120 parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did in 2005? Conduct a hypothesis test at 5% significance level.

a.What are the null and alternative hypotheses? What is the type of the test (left, right, or two tailed)?

b. Compute the test statistic (Round intermediate steps to 4 decimal places and round to 2 decimal places.)

c. Use the z table to find the P-value

d. What is her conclusion? Show detailed comparison and explanation.

In a survey of 650 community college students, 423 indicated that they have read a book for personal enjoyment during the school year. Construct a 90% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year. Use 4 non-zero decimal places in your calculations.

a.Verify the normality condition and the independence condition

b.Find the Z-alpha/2

c.Find the margin of error (ME)

d. Find the upper/lower bound and Interpret the confidence interval

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults, x is approximately normally distributed with mean of 38 and standard deviation of 12 . What is the probability that

a) x is less than 60?

b) x is between 16 and 60?

1) Bob gets the following homework grades: 2, 2, 2, 2, 2, 10, 10, 10, 10, 10 Tom gets the following homework grades: 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 Pat gets the following homework grades: 1, 1, 8, 8, 8, 8, 8, 8, 10, 10 Find the mean homework grade for each student, find the median homework grade for each student, and estimate the standard deviation for each student. You should not find the actual standard deviation using a formula. Show all work and explain how you are getting each answer.

2) Dante records the height of 25 second graders, and Maria records the height of the first 25 people who walk into McDonalds at 6pm on a Friday night. Who do you expect will have a higher mean? Who do you expect will have a higher standard deviation? Explain.