The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 13 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 9 flights arrive late.

Provide a case scenario of a problem (actual or hypothetical) that involves a continuous random variable X that follows a normal probability distribution. Ideally, it will come from your work or field of study, but it is not absolutely necessary. You will need to use the normal probability rules to solve that problem.

Important Note: Email a draft of your problem scenario early in the week to your instructor for him/her to review it and provide feedback early in the process.

Complete the following:

1. Describe the setting in your problem scenario and a short background information.
2. Define exactly what you want to solve in this scenario and your solution plan.
3. Describe the type of data you collected for solving this problem.
4. Describe possible variable(s). (Are they continuous?)
5. Describe the statistical method(s) that you used to analyze the data. (Such as numerical summaries, graphs, etc.) Provide evidence that this data follows a normal distribution.

If you use a software to get these analyses done, cut the related output and paste it on to your assignment document.

6. Provide a detailed step by step explanations of the solution to the chosen problem. In your solution, include the following:

1. Probability that the continuous random variable is greater than a specific value pertaining your problem.
2. Probability that the continuous random variable is less than a specific value pertaining your problem.
3. Probability that the continuous random variable is between two values pertaining your problem.
4. Percentile(s) of some data values.
5. Graphs to visualize your solution.

7. Explain your thinking behind your choices of using formulas, tables, charts, etc.
8. Discuss the results.
9. Utilize proper/correct APA citations in the body of the paper and in all your references, including figures/tables in your report.

1. Briefly explain Null Hypothesis H and Alternate Hypothesis. Give an example for each.

2. Briefly explain hypothesis testing process. Give an example.

Note: type it rather than handwritting.

Assignment #8: Chi-Square Test of Independence Directions:

Use the Crosstabs option in the Descriptives menu to answer the questions based on the following scenario. (Be sure to select Chi-square from the Statistics submenu and Observed, Expected, Row, and Column in the Cells submenu. Assume a level of significance of .05)

The school district recently adopted the use of e-textbooks, and the superintendent is interested in determining the level of satisfaction with e-textbooks among students and if there is a relationship between the level of satisfaction and student classification. The superintendent selected a sample of students from one high school and asked them how satisfied they were with the use of e-textbooks. The data that were collected are presented in the following table.

Student Classification (N = 126)

Satisfied Freshmen Sophomore Junior Senior

Yes 13 13 21 20

No 22 17 8 12

1. Of the students that were satisfied, what percent were Freshmen, Sophomore, Junior, and Senior? (Round your final answer to 1 decimal place).

2. State an appropriate null hypothesis for this analysis.

3. What is the value of the chi-square statistic?

4. What are the reported degrees of freedom?

5. What is the reported level of significance?

6. Based on the results of the chi-square test of independence, is there an association between e-textbook satisfaction and academic classification?

7. Present the results as they might appear in an article. This must include a table and narrative statement that reports and interprets the results of the analysis.

Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

A business school conducted a survey of companies in its state. They mailed a questionnaire to 200 small companies, 200 medium-sized companies and 200 large companies. The rate of nonresponse is important in deciding how reliable survey results are. Here are the data:

Small              Medium           Large
Response             125                       81                40
No response          75                      119              160

What is the overall rate of nonresponse? If response rate is not related to size of company, you would expect all companies, regardless of size, to have a similar response rate.

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and in the United Kingdom. Suppose that independent random samples of television ads are taken in the two countries. A random sample of 400 television ads in the United Kingdom reveals that 141 use humor, while a random sample of 500 television ads in the United States reveals that 119 use humor.

(a) Set up the null and alternative hypotheses needed to determine whether the proportion of ads using humor in the United Kingdom differs from the proportion of ads using humor in the United States.

H₀: p₁ − p₂ (Click to select)≠= 0 versus H_a: p₁ − p₂ (Click to select)=≠ 0.

(b) Test the hypotheses you set up in part a by using critical values and by setting α equal to .10, .05, .01, and .001. How much evidence is there that the proportions of U.K. and U.S. ads using humor are different? (Round the proportion values to 3 decimal places. Round your answer to 2 decimal places.)

(Reject/Do not Reject) H₀ at each value of α; (Click to select)strongextremely strongnonesomevery strong evidence.

(c) Set up the hypotheses needed to attempt to establish that the difference between the proportions of U.K. and U.S. ads using humor is more than .05 (five percentage points). Test these hypotheses by using a p-value and by setting α equal to .10, .05, .01, and .001. How much evidence is there that the difference between the proportions exceeds .05? (Round the proportion values to 3 decimal places. Round your z value to 2 decimal places and p-value to 4 decimal places.)

(Do not reject/Reject)  H₀ at each value of α = .10 and α = .05; (Click to select)somestrongvery strongextremely strongnone evidence.

(d) Calculate a 95 percent confidence interval for the difference between the proportion of U.K. ads using humor and the proportion of U.S. ads using humor. Interpret this interval. Can we be 95 percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor? (Round the proportion values to 3 decimal places. Round your answers to 4 decimal places.)

95% of Confidence Interval                      [ , ]

(Yes/No) the entire interval is above zero.

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 78% of the successful bids and 35% of the unsuccessful bids the agency requested additional information.

a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)?

b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)?

c. Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).

Alana consulted a local master beekeeper, Dr. Beekeeper, concerning the death of some of her beehives. He suggested adding a specific type of plant food, “Bee Empower” to the clover fields where the bees forage for nectar. The amount of Bee Empower (in kg) that should be added per acre of clover field is represented by:

f(x)= -9x² + 126x -45

x=kg of Bee Empower/acre

A. Find the critical value of Bee Empower for this function

B. In words, describe what this value means

C. Is this value the minimum or maximum amount of plant food needed per acre? Mathematically prove your answer.

This is for Geography Stats.

I have already found the weighted mean center of population. Which is (3.34,3.48)

and the unweighted mean center (2.94,2.48).

I need to find the Bachi's Weighted Standard Distance. I am completely lost with this part of the question. Any help would be much appreciated! Test tomorrow =(

A poll conducted between February and April of 2006 surveyed 2822 Internet users and found that 198 of them had downloaded a podcast to listen to it or view it later at least once. A similar poll in May of the same year found that 295 of 1553 Internet users had downloaded a podcast at least once. Test the null hypothesis that the two proportions are equal.

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

With the help of the Excel Exponential Smoothing tool, I was able to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3 (ie, damping factor of 0.7).

I was also able to calculate the Mean Absolute Deviation (MAD) of each of the stocks: MAD of Stock A = 1.32 MAD of Stock B = 0.37 MAD of Stock C = 0.41 MAD of Stock D = 0.26 MAD of Stock Exchange = 83.85.

The Mean Square Error (MSE) of the stocks: MSE of Stock A = 2.22, MSE of Stock B = 0.17, MSE of Stock C = 0.21, MSE of Stock D = 0.08, MSE of Stock Exchange = 7963.44.

Help me to understand the concept of Mean Absolute Percentage Error (MAPE). I realize that MAPE is the average of absolute errors divided by actual observation values. I'm wondering if this is just the MAD divided by the total observation values for a particular stock. For example, for Stock A, If my understanding is correct (which I don't think it is), the MAPE of Stock A would be 1.32 / each of the observation values individually. Or, would it be [(127.15 - 127.37) / 127.15]. Or, do I need to add up all the absolute errors for Stock A and all the actual observation values for Stock A and divide the former by the latter and then multiply by 100. As you can see, I'm confused. Please help.

Sally’s Toyota Corolla is an old car but it served her well. She is planning to take a trip to the Grand Canyon from the east coast. Before starting the trip she checks the car to determine if the car is in good mechanical condition. She is knowledgeable about cars but no expert. The null and alternative hypotheses are given below.

H0: the Corolla is in good mechanical condition

Ha: the Corolla is not in good mechanical condition

(a) What would a Type-I error be in this situation?

(b) What would a type-II error be in this situation?

(c) Which error is more consequential in this situation and why?

(d) If Sally took the Corolla out to a certified mechanic for a checkout, what would be the likely impact on the magnitude of the Type-I and Type-II errors and why?

The 4M company has a work center with a single turret lathe. Jobs arrive at this work center according to a Poisson process at a mean rate of 2 jobs per day, The lathe processing time has an exponential distribution with a mean of 0.25 day per job.

a) On average, how many jobs are waiting.in the work center?

b) On average, how long will a job stay in the center?

c).Since each job takes a big space, the waiting jobs are currently waiting in the warehouse. The production manager is proposing to add a storage space near the lathe. If an arriving job will have at least 90% chance waiting near the lathe, how big should be the storage space near the lathe?

Why is it “harder” to find a significant outcome (all other things being equal) when the research hypothesis is being tested at the .01 rather than the .05 level of significance?