1. The president of a large university has been studying the relationship between male/female supervisory structures in his institution and the level of employees’ job satisfaction. The results of a recent survey are shown in the table below. Conduct a test at the 5% significance level to determine whether the level of job satisfaction depends on the boss/employee gender relationship.

                                                                                        Boss/Employee

Size of a firm matters for implementation of supply chain management practices. It implies that larger firms very frequently implement supply chain and use advanced technologies to integrate supply chain partners. A study has reported part of the relationship between types of firm (Private and Public) and supply chain management implementation and between size of a firm (small to large, in terms of number of employees) and supply chain management implementation in International Journal of Business Modelling and Supply Chain Management (Vol. 5, 2013). The following table shows number of different sized private and public firms participated in this study:

Two following events are defined:

A: {A firm participated in this study is Private}

B: {A firm participated in this study has employees more than 49}

Find

a. P(A) and P(B)​

b. P(AUB) ​​​​​​​​​

c. P(AnB) ​​​​​​​​​

An institute reported that

68% of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members. Complete parts ​(a) through ​(d) below.

a. What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between

66

and 72​%?

0.4704

​(Type an integer or decimal rounded to four decimal places as​ needed.)

b. The probability is 70

that the sample percentage will be contained within what symmetrical limits of the population​ percentage?The probability is 70% that the sample percentage will be contained above 63​%

and below 73%

​(Type integers or decimals rounded to one decimal place as​ needed.)

c. The probability is

97% that the sample percentage will be contained within what symmetrical limits of the population​ percentage? The probability is 97% that the sample percentage will be contained above nothing​% and below nothing​%.

What's the answer to C

Is there an application of Seasonal Indices or variation in an organization or institution that you might have worked for or are familiar with?

If so,

a) Define the states of application.

b) Share the data or factors, if possible

Please provide a unique answer not regarding different product SKU's.

Runiowa is a fashion shoe company that tries to manufacture much more durable heels in 2020. The management team of Runiowa suggests two rubber materials A and B and the research team of Runiowa is asked to design an experiment to gauge whether the rubber A is more durable than the rubber B. 300 people in the US aged between 18 and 65 were randomly chosen. The rubber A is allocated at random to the right shoe or the left shoe of each individual. Then, the rubber B has been assigned to the other. For example, if Mr. Nathaniel is one of 300 people randomly chosen, then the right heel of Mr. Nathaniel is randomly assigned to be made with the rubber A and then his left heel is to be made with the rubber B. The research team measures the amounts of heel wear both the rubber A (wA) and the rubber B (wB) in each individual and records the difference wA − wB of 300 individuals. Even though the individuals are heterogeneous with different heights and weights, those individual heterogeneities will not obscure the comparison of treatment groups by focusing on the paired differences of each individual. Also as long as the heel materials are randomly assigned for each individual, there has been no restrictions on shoe styles. Note that the age of subjects is ranging from 18 to 65. In this way, researchers compare treatments within blocks controlling heterogeneity of individuals. The research team also repeats this experiment design with 300 people in the US aged between 18 and 65 chosen at random.

Question:

What are the experimental units?

What is the control?

Hoe much replication was used?

How was randomization used?

The variable Hours Studied represents the number of hours a student studied for their final exam and the variable Final Exam Grade represents the final exam score the student received on their final exam (out of 100 points).An introduction, explanation/interpretation of your analysis, and a conclusion.

Hours studied- 1, 0, 7, 9, 9, 5, 4, 2, 11, 7, 13, 3, 3, 1, 9, 7, 5, 0, 2, 8

Final Exam grade 70, 54, 81, 92, 90, 78, 75, 68, 98, 84, 100, 78, 79, 72, 88, 85, 83, 55, 73, 86

1) What are the explanatory and response variables?

2) Determine the mean, standard deviation, and five-number summary for each variable.

3) What is the value of the linear correlation coefficient?

4) Based on the value of the linear correlation coefficient, is the correlation between Hours Studied and Final Exam Grade strong or weak? Why?

5) Determine the equation of the linear regression line.

6) Use your regression equation to predict the final exam grade if a student randomly selected studied for six hours.

7) Generate a scatterplot with a fitted regression line.

8) Interpret the meaning of the slope of the regression line in terms of Hours Studied and Final Exam Grade.

9) What is the y-intercept of the regression line and what does it mean regarding Hours Studied and Final Exam Grade? Is this realistic?

10) Use your regression equation to predict the final exam grade if a student randomly selected studied for thirty hours. Is this realistic?

11) What is the value of the coefficient of determination and what does it mean regarding this data set?

Fill amounts of jars of peanuts from a certain factors are known to follow a Normal distribution with mean 454g and standard deviation 15g. Suppose that a random sample of 8 jars is taken. What is the probability that the average weight of this sample is between 451g and 458g?

An advertising executive wants to estimate the mean weekly amount of time 18- to 24-year-olds spend watching traditional television in a large city. Based on studies in other cities, the standard deviation is assumed to be 10 minutes. The executive wants to estimate, within 99% confidence, the mean weekly amount of time within ±3 minutes.

a. What sample size is needed?

b. If 95% confidence is desired, how many 18- to 24-year-olds need to be selected?

c. If she wants to estimate the mean within ±2 minutes, what size is needed for a 99% and 95% confidence level, respectively? Please show work

Let X be normally distributed with mean μ = 4.1 and standard deviation σ = 3.

b. Find P(5.5 ≤ X ≤ 7.5).

c. Find x such that P(X > x) = 0.0485.

7.5 Apartment rents. Refer to Exercise 7.1 (page 360). Do these data give good
reason to believe that the average rent for all advertised one-bedroom apartments
is greater than $650 per month? Make sure to state the hypotheses, find the t
statistic, degrees of freedom, and P-value, and state your conclusion using the
5% significance level.

Reference:

7.1 One-bedroom rental apartment. A large city newspaper contains several
hundred advertisements for one-bedroom apartments. You choose 25 at random
and calculate a mean monthly rent of $703 and a standard deviation of $115.
(a) What is the standard error of the mean?
(b) What are the degrees of freedom for a one-sample t statistic?

Research is defined as “a systematic investigation into and study of materials and sources in order to establish facts and research new conclusions”. Research also included designing research projects and performing statistical analysis. Design a research project that you feel would benefit the Clemson University Athletic Department. The research question is: What are the positive and negative effects of caffeine on athletic performance?

Included within your design and your research question, please provide a purpose statement, at least two hypotheses, a research question, a null hypothesis, the dependant and independant variable, a description of the type of data you will gather and how you will gather it, who is your population and how will you sample that population, and the type of statistical analysis you would use to analyze the data. If you had to use correlation and t test as the statistical tests , WHY and HOW would you run this test. What would be the results of this test? What will you measure in order to determine the performance?

Finally, please also discuss the potential benefit(s) the study would have on the athletic department.

7.11 95% confidence interval for the difference in taste. To a restaurant
owner, the real question is how much difference there is in taste. Use the preced-
ing data to give a 95% confidence interval for the mean difference in taste scores
between oil-free and hot-oil frying.

Reference:

7.10 Oil-free deep fryer. Researchers at Purdue University are developing an
oil-free deep fryer that will produce fried food faster, healthier, and safer than hot oil.4
As part of this development, they ask food experts to compare foods made with hot
oil and their oil-free fryer. Consider the following table comparing the taste of hash
browns. Each hash brown was rated on a 0 to 100 scale, with 100 being the highest rat-
ing. For each expert, a coin was tossed to see which type of hash brown was tasted first.
Expert 1 2 3 4 5
Hot oil 78 83 61 71 63
Oil free 75 85 67 75 66
Is there a difference in taste? State the appropriate hypotheses, and carry out a
matched pairs t test using a(alpha) = 0.05

The attached Excel file has a sample of tuition rates at 10 colleges in the US. Based on this sample consider the hypothesis that average tuition is $7500.   Ho: µ=7500. Calculate the t value for this test. Enter your answer to 3 decimal places.

The attached Excel file has a sample of tuition rates at 10 colleges in the US. Based on this sample consider the hypothesis that average tuition is at least $8000. Ho: µ≥8000. Calculate the t value for this test. Enter your answer to 3 decimal places.

Consider the following statistical study and: a) Identify the population and the population parameter of interest. b) Describe the sample and sample statistic for the study. c) Identify the type of study. d) Discuss what additional facts you would like to know before you believed the study or acted on the results of the study. A study done at the Center for AIDS and STD at the University of Washington tracked the survival rates of 17,517 asymptomatic North American patients with HIV who started drug therapy at different points in the progression of the infection. It was discovered that asymptomatic patients who postponed antiretroviral treatment until their disease was more advanced faced a higher risk of dying than those who had initiated drug treatment earlier (New England Journal of Medicine).

Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here:

For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 35/50 = 0.7, or 70%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 35/61 = 0.57, or 57%, of the cherry cabinets if it worked only on cherry cabinets.

1. Formulate a linear programming model that can be used to determine the proportion of the oak cabinets and the proportion of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects.
   

   Let	O1 = proportion of Oak cabinets assigned to cabinetmaker 1
   	O2 = proportion of Oak cabinets assigned to cabinetmaker 2
   	O3 = proportion of Oak cabinets assigned to cabinetmaker 3
   	C1 = proportion of Cherry cabinets assigned to cabinetmaker 1
   	C2 = proportion of Cherry cabinets assigned to cabinetmaker 2
   	C3 = proportion of Cherry cabinets assigned to cabinetmaker 3

   Min

   O1

   +

   O2

   +

   O3

   +

   C1

   +

   C2

   +

   C3

   s.t.

   O1

   C1

   ≤

   Hours avail. 1

   O2

   +

   C2

   ≤

   Hours avail. 2

   O3

   +

   C3

   ≤

   Hours avail. 3

   O1

   +

   O2

   +

   O3

   =

   Oak

   C1

   +

   C2

   +

   C3

   =

   Cherry

   O1, O2, O3, C1, C2, C3 ≥ 0

2. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places.
   

   	Cabinetmaker 1	Cabinetmaker 2	Cabinetmaker 3
   Oak	O1 =	O2 =	O3 =
   Cherry	C1 =	C2 =	C3 =

   
   Total Cost = $  
   
3. If Cabinetmaker 1 has additional hours available, would the optimal solution change?
   
   
   
   Explain.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. If Cabinetmaker 2 has additional hours available, would the optimal solution change?
   
   
   
   Explain.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
5. Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places.
   

   	Cabinetmaker 1	Cabinetmaker 2	Cabinetmaker 3
   Oak	O1 =	O2 =	O3 =
   Cherry	C1 =	C2 =	C3 =

   
   Total Cost = $  
   
   Explain.