Using the data from your organization, identify an example where the quantitative process of “decision making under uncertainty” could assist with a decision.

a)      Define the states of nature and estimate probabilities for each state of nature.

b)      Organize data in a payoff table.

c)      Determine the expected payoff of each alternative.

d)     Determine the best alternative.

e)      Calculate the value of perfect information.

A fair coin is flipped until a head appears. Let the number of flips required be denoted N (the head appears on the ,\1th flip). Assu1ne the flips are independent. Let the o utcon1es be denoted by k fork= 1,2,3, . ... The event {N = k} 1neans exactly k flips are required. The event {,v;;, k} n1eans at least k flips are required.

a. How n1any o utcon1es are there?

b. What is Pr[N = k] (i.e., the probability of a sequence of k - 1 tails followed by a heads)? (Hint: write a gene ral expression for Pr[N = k] for any k = 1,2,3, .. . )

c. Show the probabilities sum to l (i.e., I:f: 1 Pr[,v = k] = 1).

d. What is Pr [ N ;;, I] for all I;;: l?

e. What is Pr[N s /] for all I;;: l?

f. Do the answers to tl1e previous two parts sum to l? Should they?

In a recent survey, 456 out of 600 people surveyed think that the subject of calculus is difficult.

1. What is the margin of error for a 90% confidence interval for the percent of people that find calculus difficult?

2. Calculate the 90% confidence interval to determine whether the sample data supports the conclusion that a majority of people think calculus is difficult.

1. A quality characteristic of interest for a tea-bag filling process is the weight of the tea in the individual bags. In this example, the label weight on the package indicates that the mean amount is 5.5 grams of tea in a bag. If the bags are underfilled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. On the other hand, if the mean amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of tea, and the extremely fast filling operation of machine (approximately 170 bags per minute). Here is the sample of 50 tea bags produced in an 8-hour shift

5.25, 5.29, 5.32, 5.32, 5.34, 5.36, 5.40, 5.40, 5.40, 5.41, 5.42, 5.42, 5.44, 5.44, 5.44, 5.45, 5.45, 5.46, 5.47, 5.47, 5.49, 5.50, 5.50, 5.50, 5.51, 5.52, 5.53, 5.53, 5.53, 5.53, 5.54, 5.54, 5.55, 5.55, 5.56, 5.56, 5.57, 5.57, 5.57, 5.58, 5.58, 5.58, 5.61, 5.61, 5.62, 5.63, 5.65, 5.67, 5.67, 5.77

a. What is the Null and alternative Hypothesis

b. What are the n and the d.f for this problem

c.What test and formula should use to test the null hypothesis

d. is there evidence that the mean amount of tea per bag is different from 5.5 grams per bag (use σ = .01)

e. Construct a 99% confidence interval estimate for the population mean weight of the tea bags. Interpret this interval

use in excel if possible

As Kevin Rudy explains in “Moneyball Shows the Power of Statistics,” “[t]he movie Moneyball tells the story of how Oakland Athletics general manager Billy Beane used statistics to assemble and manage his baseball team.” 1Whether or not you have seen the movie, you can probably guess this approach was met with resistance. When Billy Beane first used this approach, managers took other factors into consideration. For example, little known or unknown players were not typically recruited over well-known, established players.

1. Explain whether or not you think assembling and managing a baseball team, or any team for that matter, based solely on statistics is an effective course of action.

2.Are there other factors that should be considered, and if so, which ones?

3. Do you think statistics-based recruiting is an effective course of action? Why or why not?

A population has a mean of 800 and a standard deviation of 200. Suppose a sample of size 400 is selected and x is used to estimate μ. (Round your answers to four decimal places.)

(a) What is the probability that the sample mean will be within ±5 of the population mean?

(b) What is the probability that the sample mean will be within ±10 of the population mean?

A simple random sample of 90 items resulted in a sample mean of 70. The population standard deviation is

σ = 15.

(a)

Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)

to

(b)

Assume that the same sample mean was obtained from a sample of 180 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)

to

(c)

What is the effect of a larger sample size on the interval estimate?

A larger sample size provides a smaller margin of error.A larger sample size provides a larger margin of error.    A larger sample size does not change the margin of error.

Select one (1) project from your working or educational environment in which you would use the confidence interval technique for the process. Next, speculate on one to two (1-2) challenges of utilizing such a technique in the process and suggest your strategy to mitigate the challenges in question.

What does the "P-value" represent? Examples

Describe a correlation analysis, and provide an example of one. Provide examples of dependent and independent variables, as well.

Please type answer, can't see written answers well.

Also PLEASE PROVIDE BELL SHAPED CURVE** That is the part I struggle with the most.

The airlines industry measures fuel efficiency by calculating how many miles one seat can travel, whether occupied or not, on one gallon of jet fuel. The following data show the fuel economy, in miles per seat for 17 randomly selected flights on Delta and United. Assume the two population variances for fuel efficiency for the two airline are equal.

Delta

United

a. Conduct a the 95% confidence interval estimate of the population?

b. Perform a hypothesis test using α = .05 to determine if the average fuel efficiency  differs between the two airlines.

c. Determine the p-value and interpret the results.

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer. SETUP: Is it reasonable to believe that people with body fat less than 20 (%) are of different height than the people with body fat of more than 20 (%). Given the data your job is to answer this question.

I. What test/procedure did you perform? (6.66 points)

• a. One sided T-test
• b. Two sided T-test
• c. Regression
• d. Confidence interval

II. Statistical interpretation? (6.66 points)

• a. Since P-value is small we are confident that the slope is not zero.
• b. Since P-value is small we are confident that the averages are different.
• c. Since P-value is too large the test is inconclusive.
• d. None of these.

III. Conclusion? (6.66 points)

• a. Yes, this is a reasonable belief.
• b. No, we cannot confirm that this is a reasonable belief.

Given a normal distribution with mean population of 51 and standard devitation of 8​, and given you select a sample of n=100​, complete parts​ (d).

d. There is a 30​% chance thatt X(w/bar above) is above what​ value? (Type an integer or decimal rounded to two decimal places as​ needed.)

a.   Suppose that 5 % of the items produced by a factory are defective. If 5 items are chosen at random, what is the probability that none of the items are defective? Write your answer as a decimal accurate to three decimal places.

b. Suppose that 7.9 % of the items produced by a second factory are defective. If 5 items are chosen at random from the second factory, what is the probability that exactly one of the items is defective? Write your answer as a decimal accurate to three decimal place

c. Suppose that 10.8 % of the items produced by a third factory are defective. If 5 items are chosen at random from the third factory, what is the probability that exactly two of the items are defective? Write your answer as a decimal accurate to three decimal places.

d. Suppose that 7.3 % of the items produced by a fourth factory are defective. If 5 items are chosen at random from the fourth factory, what is the probability that at least two of the items are defective? Write your answer as a decimal accurate to three decimal places.

e. Suppose that 14.2 % of the items produced by a fifth factory are defective. If 4 items are chosen at random from the fifth factory, what is the expected value (or mean value) for the number of defective items? Write your answer as a decimal accurate to three decimal places.

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer. SETUP: Is it reasonable to claim that cars with higher city MPG have also higher Highway MPG? Given the data your job is to help answer this question.

I. What test/procedure did you perform? (6.66 points)

• a. One sided T-test
• b. Two sided T-test
• c. Regression
• d. Confidence interval

II. Statistical interpretation? (6.66 points)

• a. Since P-value is small we are confident that the slope is not zero.
• b. Since P-value is small we are confident that the averages are different.
• c. Since P-value is too large the test is inconclusive.
• d. None of these.

III. Conclusion? (6.66 points)

• a. Yes, we confirm that this was a reasonable claim.
• b. No, we cannot confirm that this was a reasonable claim.

Use engine size to predict the car’s width. Answer the questions.

I) For each additional 3.0 liter in engine size how much the car’s width will change? (11.11 points)

• a. It will increase by 2.42 units.
• b. It will increase by 7.27 units.
• c. It will increase by 68.2 units.
• d. It will increase by 63.3 units.
• e. Not applicable.

II) After performing the regression analysis you are asked to pick one number that would best answer the question: Are these two variables, engine size and car width, related or not? What is this number and why? (11.11 points)

• a. The number is the slope and it clearly indicates the relation: For each additional liter in engine size the car’s width increases.
• b. This number is R-square and since it is not close to 1 we cannot claim that these two variables are related.
• c. The number is the P-value, which in this case is very low indicating a strong probability that the two variables are related.
• d. None of these.

III) Given a car that has engine size of 2.0 liters use regression analysis and all available information in there, in order to predict this car’s width. What is your interval prediction?   (11.11 points)

• a. [66.36, 70.09]
• b. ± 1.8
• c. 68.2
• d. 63.3
• e. Not applicable