An urn contains 5 blue marbles and 4 red marbles. You draw a certain number of marbles from the urn at random with replacement . . .

(A) You win $243.00 if you draw more blue marbles than red marbles. Assuming that you want to win, which is better: drawing 20 marbles or 200 marbles? Explain your answer briefly.

(B) You win $177.00 if the percentage of red marbles that you draw is less than 42%. Assuming that you want to win, which is better: drawing 10 marbles or 100 marbles? Explain your answer briefly.

Many fast-food restaurants use automatic soft-drink dispensing machines that fill cups once an order is placed at a drive-through window. A regional manager for a fast-food chain wants to determine if the machines in her region are dispensing the same amount of product. She samples four different machines and measures a random sample of 16-ounce drinks from each machine. Here is the data she collects (in ounces):

a) “Number of ounces” is a quantitative variable. Is it discrete or continuous?

b) “Number of ounces” is what level of measurement?

c) Is this a designed experiment or an observational study? Briefly explain.

d) At the 5% Level of Significance, determine whether or not the data indicate that the mean amount dispensed from the machines is not the same, by doing each of the following:

1) Write the Hypotheses.

2) Use your calculator to do a one-way ANOVA test. Explain in some detail how the results of the test lead you to reject or not reject the null hypothesis.

3) Write a formal conclusion.

e) Using the language of our textbook on bias (way back in Section 1.5), name at least one type of bias that might be present in this research. Briefly explain.

A consumer advocacy group published a study of labeling of seafood sold in three U.S. states. The study found that 15 of the 25 ​"red snapper" packages tested were a different kind of fish. Assume that the study used a simple random sample. Complete parts a through c below. ​

a) Are the conditions for creating a confidence interval​ satisfied? Explain.

A. ​Yes, because the sample is a simple random​ sample, the sample proportion is between​ 10% and​ 90%, and there are at least 20 expected​ "successes" and 20 expected​ "failures."

B. ​Yes, because the sample is a simple random​ sample, the sample is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

C. ​No, because the sample is a simple random​ sample, the sample is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

D. ​No, because the sample is a simple random​ sample, the sample proportion is between​ 10% and​ 90%, and there are at least 20 expected​ "successes" and 20 expected​ "failures." ​

b) Construct a 95​% confidence interval for the proportion of​ "red snapper" packages that were a different kind of fish. (___________ , _____________) ​(Round to three decimal places as​ needed.) ​

c) Explain what the confidence interval from part​ (b) says about​ "red snapper" sold in these three states. Select the correct choice below and fill in the answer boxes within your choice. ​(Round to one decimal place as​ needed.)

A) One is 95% confident that between ________% and ______________% of all red snapper sold in food stores and restaurants in these states is not actually re snapper.

B) 98% of the time, the true proportion of red snapper sold in these three states is falsely labeled is between__________% and ________%.

C) One is 95% confident that between ______% and ________% of all red snapper purchased for the study in these states was not actually red snapper.

D) No, because the sample is a simple random sample, the sample proportion is between 10% and 90% and there are at least 20 expected "successes" and 20 expected "failures".

Use facts and examples from "Double Jeopardy: To Be Black and Female" and also from "Mirta Vidal Reports on the Rising Consciousness of the Chicana about her Special Oppression" to write a couple of paragraphs to the prompt below. Write a few paragraphs to explain how the experiences of Black and Chicana women were different than that of white women during the second wave of the Women's Movement. What are some methods used to oppress these women of color? **You must use critical thinking and analysis to answer this question. The strongest answers will also place this into historical context and make connections with other things that were covered in class. Use specific examples and details to support what you state. Your answer should be thorough and concise.

History of the women 111

Use the Library or the Internet to research and find a situation where probabilities might be useful in daily life or in your chosen career. Complete the following:

Explain in detail how probabilities are used in the situation you chose.What makes probabilities useful in this situation? Do these probabilities affect decision making in this situation? Explain your answer.Give a specific example of how probabilities are used in this situation.How are probabilities important to decision making in this situation? If they are not,

!!!!!!!!!!!Please explain in detail how you find the answers!!!!!!!!!!!

3. As a further measure for the effectiveness of the medical program, FAU decides to administer the same test to five students in their first year, and then again when they graduate the program: Use the scores below to conduct a t-test and determine whether the scores significantly change over time.

First Year      Graduation

85    88

88    93

82    86

92    95

91    96

3B. State the t-statistic and cutoff score (.05-test, 2-tailed) in the t-distribution

3C. Was the test significant?

A telephone company claims that less than 20% of its customers have at least two telephone lines. The company selects a random sample of 500 customers and finds that 88 have two or more telephone lines. Use LaTeX: \alpha α = 0.05 and the P-value method. Correctly state a) your conclusion about what to do with H0 AND b) your conclusion about the claim that is being made.

There has been much debate in recent years about the role of the Federal Reserve System. Explain in detail how the Federal Reserve functions and influences policy decisions.

Grades and AM/PM Section of Stats: There were two large sections of statistics this term at State College, an 8:00 (AM) section and a 1:30 (PM) section. The final grades for both sections are depicted in the contingency table below.

Observed Frequencies: O_i's

The Test: Test for a significant dependent relationship between grades and the section of the course. Conduct this test at the 0.05 significance level.

(a) What is the test statistic? Round your answer to 3 decimal places.

χ²

=

(b) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(c) Choose the appropriate concluding statement.

We have proven that grades and section of the course are independent.

The evidence suggests that there is a significant dependent relationship between grades and the section of the course.    

There is not enough evidence to conclude that there is a significant dependent relationship between grades and the section of the course.

1. Problem 16-09

   The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association Developmental League (NBA-DL). Because a player in the NBA-DL is still developing their skills, the number of points he scores in a game can vary. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the table below.

   Player	Iowa Energy	Maine Red Claws
   1	[5, 20]	[7, 12]
   2	[7, 20]	[15, 20]
   3	[5, 10]	[10, 20]
   4	[10, 40]	[15, 30]
   5	[6, 20]	[5, 10]
   6	[3, 10]	[1, 20]
   7	[2, 5]	[1, 4]
   8	[2, 4]	[2, 4]

   1. Develop a spreadsheet model that simulates the points scored by each team. What is the average and standard deviation of points scored by the Iowa Energy? If required, round your answer to one decimal place.
      
      Average =
      
      Standard Deviation =
      
      What is the shape of the distribution of points scored by the Iowa Energy?
      
      
      
   2. What is the average and standard deviation of points scored by the Maine Red Claws? If required, round your answer to one decimal place.
      
      Average =
      
      Standard Deviation =
      
      What is the shape of the distribution of points scored by the Maine Red Claws?
      
      
      
   3. Let Point Differential = Iowa Energy points - Maine Red Claw points. What is the average point differential between the Iowa Energy and Maine Red Claws? If required, round your answer to one decimal place.
      
      
      
      What is the standard deviation in the point differential?
      
      
      
      What is the shape of the point differential distribution?
      
      
      
   4. What is the probability of that the Iowa Energy scores more points than the Maine Red Claws? If required, round your answer to three decimal places.
      
      
      
   5. The coach of the Iowa Energy feels that they are the underdog and is considering a "riskier" game strategy. The effect of the riskier game strategy is that the range of each Energy player's point production increases symmetrically so that the new range is [0, original upper bound + original lower bound]. For example, Energy player 1's range with the risky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Energy point total?
      
      Average =
      
      Standard Deviation =
      
      Explain.
      
      The input in the box below will not be graded, but may be reviewed and considered by your instructor.
      
      
      
      How is the probability of the Iowa Energy scoring more points that the Maine Red Claws affected? If required, round your answer to three decimal places.
      
      Probability =
      
      Explain.
      
      The input in the box below will not be graded, but may be reviewed and considered by your instructor.