An urn contains 5 balls, two of which are marked $1, two $4, and one $10. A player is to draw two balls randomly and without replacement from the urn. Let X be the sum of the amounts marked on the two balls. Find the expected value of X.

Side note:

I know Rx={2,5,8,11,14}

and P(X=2) = 1/10 ... etc

I just need a proper explanation for finding the values of P(X=2), P(X=5), etc. Thanks!

The proportion of public accountants who have changed companies within the last three years is to be estimated within 5%. The 99% level of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 23. (Use z Distribution Table.) (Round the z-values to 2 decimal places. Round up your answers to the next whole number.)

a. To update this study, the files of how many public accountants should be studied? b. How many public accountants should be contacted if no previous estimates of the population proportion are available?

Consider the following studies:
Study 1: A study was conducted to investigate the effects of alcohol consumption on handeye
co-ordination. 200 people were interviewed and their level of alcohol consumption
over the previous five years was assessed and classified as either low, medium or high.
Each person was then given a series of tasks resulting in a hand-eye co-ordination score.

Study 2: A study was conducted to investigate the efficacy of a new iron tablet compared to a
currently used iron tablet. It is known that the level of efficacy for iron tablets is different
for males and females. 200 people were available for the study. First, they were divided
into males and females. Then these two groups were randomly split in half – one half was
given the new tablet, while the other half was given the existing tablet. At the start of the
study, all participants were given blood tests and their iron levels measured. After six
weeks of taking the iron tablets, they were given another blood test and their iron levels
measured again. For each subject, the difference in iron levels was recorded. The average
of the differences were then compared separately for males and females.

(a) Answer the following questions FOR EACH study:
(i) Identify the groups that are being compared. (I.e., what treatments or factors of interest
are being compared?) DO NOT also say what is being measured to make the
comparison – you do this in (ii).
(ii) What is being measured to compare these groups? ONLY describe the variable being
measured. DO NOT also mention the groups being compared – you do this in (i).
(iii) Would you describe the study as an experiment or an observational study?
- If it was an experiment, what part of the study design led you to this conclusion?
- If it was an observational study, could an experiment have been easily carried out
instead? If so, briefly explain how. If not, briefly explain why not

The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $38, and the standard deviation for female consumers is assumed to be $19.

1. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
   
2. At 99% confidence, what is the margin of error (to 2 decimals)?
   
3. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
   (  ,   )

At α= .05, test to see if there is a significant difference among the average bills of all the homes (in a city) using three forms of heating. Use both the critical and p-value approaches.  Be sure to include your hypotheses, critical values, results, and conclusions in the language of the problem.

The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with 2 levels of factor A, 3 levels of factor B, and n = 6 participants in each treatment condition.

A. Fill in all missing values in the table. Show your work (i.e., all computational steps for finding the missing values). Hint: start with the df values.

B.  Do these data indicate any significant effects (assume p < .05 for hypothesis testing of all three effects)?

• the null hypothesis H₀ & the alternative hypothesis H₁
• the critical F value used for the decision about H₀
• if the difference is statistically significant, the computed effect size, η²
• the conclusion in APA style format

Between treatments: SS=75 df=? MS=?
Factor A: SS=? df=? MS=? Fa=
Factor B: SS=? df= ? MS= 15 Fb=

AXB: SS=? df=? MS=? Faxb=6.00

within treatments: SS=? df=? MS=?

total: SS=165 df=?

As part of an annual review of its accounts, a discount brokerage selects a random sample of 28 customers. Their accounts are reviewed for total account valuation, which showed a mean of $32,300, with a sample standard deviation of $8,500. (Use t Distribution Table.) What is a 98% confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.) 98% confidence interval for the mean account valuation is between $ ___ and $ ___

HYPOTHESIS TESTING SUMMARY ACTIVITY

Part 1: Overview of the Hypothesis Test for the Population Proportion Answer the following questions:

1) The general form of the test statistic for the hypothesis test for a population proportion is shown below. Label the different components of the test statistic.

2) For the following situations, state the null and alternative hypothesis. Then determine whether the alternative hypothesis is one-sided or two-sided.

a) A toy manufacturer claims that 23% of the 14-year-old residents of a certain city own a skateboard. A sample of fifty 14-year-olds shows that nine own a skateboard. Is there enough evidence to show that the percentage has changed?

b) At a large university, a study found that 25% of the students who commute travel more than 14 miles to campus. Recently, the university built more housing closer to campus so they believe that the proportion has decreased.

c) For students who first enrolled in two-year public institutions in fall 2007, the proportion who earned a bachelor’s degree within 6 years was 0.399. The president of Joliet Junior College believes that the proportion of students who enroll in her institution have a higher completion rate.

3) Use the information in question 2a (toy manufacturer) to answer the following questions.

a) Calculate the test statistic and draw a diagram with a normal curve to represent the sampling distribution of ??� in the context of this situation.

b) If the sample size of the survey was increased, would the test statistic increase or decrease? Would it give us more or less evidence against H0 ?

A manager at a company that manufactures cell phones has noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one​ day's run seems to have no bearing on the next day.

Question:

​a) What model might you use to model the number of faulty cell phones produced in one​ day?

​b) If the mean number of faulty cell phones is 3.4 per​ day, what is the probability that no faulty cell phones will be produced​ tomorrow?

​c) If the mean number of faulty cell phones is 3.4 per​ day, what is the probability that 3 or more faulty cell phones were produced in​ today's run?

A physical therapist claims that one​ 600-milligram dose of Vitamin C will increase muscular endurance. The table available below shows the numbers of repetitions 1515 males made on a hand dynamometer​ (measures grip​ strength) until the grip strengths in three consecutive trials were​ 50% of their maximum grip strength. At α=0.01 is there enough evidence to support the ​ therapist's claim? Assume the samples are random and​ dependent, and the population is normally distributed.

1)Calculate sd (Round to one decimal place as​ needed.)

2)Calculate the test statistic (Round to one decimal place as​ needed.)

3)Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

A laboratory technician claims that on average it takes her no more than 7.5 minutes to perform a certain task. A random sample of 20 times she performed this task was selected and the average and standard deviation were 7.9 and 1.2, respectively. At α = 0.05, does this constitute enough evidence against the technician's claim? Use the rejection point method.

Kohl’s wishes to investigate the relationship between level of advertising, coupon value and sales. Kohl’s advertises several times a month and includes a coupon (in dollars) with each advertisement. The value of the coupon remains the same in a month but varies from month to month. Kohl’s expects that the number advertisements and coupon value have a positive impact on sales. In addition, Kohl’s expects that the impact of advertisements increases as the coupon value increases. Kohl’s collects the sales (in thousands of dollars), number of ads and coupon value for the last one year. The data is in Kohls.sav. Express the model that the company must use, state the null and alternate hypothesis, estimate the model and provide interpretation. When the manufacturer advertises 5 times in a month and includes a $3 coupon, what is the expected sales? Please show me you SPSS Data.

Sales   Ads   CouponValue
110.54   3   4
209.83   13   2
256.74   13   3
157.86   13   1
174.32   8   3
208.69   13   4
178.57   15   1
89.34   3   3
71.58   3   2
295.77   15   3
100.65   8   1
239.03   15   2

Clearly explain what it means for a set of events to form a partition of a sample space.

Give an example of a random experiment which has a sample space for which you can define five events which together form a partition. Clearly state your choice of experiment, the resulting sample space and the five events which form the partition. State any assumptions you have made.

1. Walden University claims that its faculty members spend 11.0 hours in the classroom teaching per week on
average. You work for a student newspaper and are asked to test this claim at the 0.10 level of significance.
Assume that average classroom teaching time per week has a fairly Normal distribution. A sample of classroom
hours for randomly selected faculty members is:
11.8 8.6 12.6 7.9 6.4 10.4 13.6 9.1
a. What are the null and alternative hypotheses?
b. Find an appropriate test statistic and associated p-value.
c. Based on your sample data, would you reject H0? Explain.
d. What does this mean in terms of the problem?

Please use the Ti-83/84 to solve

Step 1: Identify and Solve a Typical Problem
There are a number of typical models in the Operations Research field which can be applied to a wide range of supply chain problems. Select one of the following typical models:
• Travelling Salesperson Problem (TSP)
• Multiple Traveling Salesman Problem (mTSP)
• Knapsack Problem
• Vehicle Routing Problems (VRP)
• Job Shop Scheduling
• Parallel Machine Scheduling
• Christmas lunch problem
• Newsvendor problem
• Pickup and delivery
• Travelling thief problem
• Eight queens problem
• Minimum Spanning Tree
• Hamiltonian path problem

1.1. Background:
• Provide a detailed explanation of the selected problem.

1.2. Model
• Provide typical mathematical model of the selected problem and clearly explain different aspects of the model (e.g. decision variable, objective function, constraints, etc.)

1.3. Solving an Example
• Develop a mathematical model for a workable and reasonable size of the problem.
– For many typical problems, when size of the problem increases, it becomes NP-Hard. In other words, your computer will not be able to solve it mathematically. Therefore, ‘workable and reasonable size’ here means that size of the selected problem should not be too small or too large.
• Solve the problem in Excel and transfer your solution to Word. It is required that details and steps of getting the solution are provided in the Word document.
• Interpret the findings and discuss.

Step 2: LR on Application of Selected Typical Model in Design and Analysis of Supply Chain
• Identify at least 5 peer reviewed articles in which your selected typical problem has been employed to address knowledge gaps in supply chain field.
– At least one of the selected articles should be published after 2010. • Write a comprehensive literature review on the application of “your selected” typical model in design and analysis of supply chain and address the following (but not limited to) points:
- What type of problems in supply chain can be addressed by the selected typical problem?
– Compare similarities and differences of selected articles.
– Discuss the suitability of using the selected typical model in design/analysis of various supply chains. – What are the limitations of your selected typical problem? – Undertaking any additional critical and/or content analysis on the application of selected typical problem in design and analysis of supply chain is highly recommended.

Step 3: Summary of Findings

• A summary of findings regarding the strengths and weaknesses of the selected typical problem in design and analysis of supply chain should be summarised in this section.