Assessment 3 – Graphical LP                                                                         

You are given the following linear programming problem.

            Maximize Z =.            $46X1 + $69X2

                        S.T.                  4X1 + 6X2      < 84

                                                2X1 + 1 X2     > 20

                                                4X1                 < 60

Using graphical procedure, solve the problem. (Graph the constraints and identify the region of feasible solutions). What are the values of X1, X2 ,S1, S2, S3, and the value of the objective function (Z) at optimum? If there are multiple optimum solutions, please give two of the optimum solutions.

Optimum solution 1:

X1 =                X2 =                S1 =                 S2 =                 S3 =                 Z =                 

Optimum solution 2: (if there is a second optimum solution)

X1 =                X2 =                S1 =                 S2 =                 S3 =                 Z =                 

Find the mean, median, and mode of the following data: 0.38, 0.52, 0.55, 0.32, 0.37, 0.38, 0.38, 0.35, 0.29, 0.38, 0.28, 0.39, 0.40, 0.38, 0.38, 0.38 Mean: Median: Mode:

Given the following data and Standard Deviation, calculate the %CV: 26, 52, 37, 22, 24, 45, 58, 28, 39, 60, 25, 47, 23, 56, 28 SD = 14.0

A fair coin is tossed repeatedly until it has landed Heads at least once and has landed Tails at least once. Find the expected number of tosses.

Heights of 10 year olds. Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Round all answers to two decimal places.

1. What is the probability that a randomly chosen 10 year old is shorter than 57 inches?

2. What is the probability that a randomly chosen 10 year old is between 61 and 63 inches?

3. If the shortest 15% of the class is considered very tall, what is the height cutoff for very tall?  inches

4. What is the height of a 10 year old who is at the 24 th percentile?  inches

Using dataset "PlantGrowth" in R (r code)

Construct a 95% confidence interval for the true mean weight.

Interpret the confidence interval in in the context of the problem.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of eighteen 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)

(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.

1. Define the following terms:

A. Contingency table

B. Chi-square test

2. List the assumptions required to perform a chi-square test?

The below age variable was inputted into SPSS and the descriptive statistics output generated. I did the interquartile range (39) to try and answer Question #4: Are there outliers among the values of age? provide a rationale for your answer. need help determining the Q1, Q3 if this is the correct approach to answer this questions and respond to what's the rationale?

Age variable
42
41
56
78
86
49
82
35
59
37

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 84 students in the highest quartile of the distribution, the mean score was x = 178.30. Assume a population standard deviation of σ = 7.47. These students were all classified as high on their need for closure. Assume that the 84 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

Math 473: R Homework #4 Name: Due: Thursday, November 7th at the beginning of class; if your homework is submitted at the end of class or later, it will be considered late. Please print this sheet and staple it to the front of your homework. You will not receive any credit for your program if it does not run, if you did not call the program from the R Console window, you call your program more than once from the R Console window, or your program is not done 100% in R. If you write your program line by line at the R prompt, or copy and paste it into the R prompt or submit more than one R program you will not receive any credit. You will not receive any credit for your program if your font is too small (less than 8) to be readable. You will not receive any credit if you do not use the “list” command or a command that performs the same function as “list”. See previous templates for examples. Write one R program to answer the following questions: 1. 48% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Determine the probability that the number of men who consider themselves baseball fans is exactly eight. 2. Fifty-five percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Determine the probability that the number of households that say they would feel secure is more than five. 3. 32% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Determine the probability that the number of adults who say cashews are their favorite nut is at most two. 4. 29% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Determine the probability that the number of college students who say they uses credit cards because of the rewards program is between two and five inclusive. 5. Sixty-six percent of pet owners say they consider their pet to be their best friend. You randomly select 11 pet owners and ask them if they consider their pet to be their best friend. Determine the probability that the number of pet owners who say their pet is their best friend is at least eight. Type a comment next to each line in the R program. The comments should describe what each line does. Hint: See the Probability Distributions handout on Blackboard. Hint: Use the “list” command at the end of the program (see the dice template); assign your answers to variables. Submit a printed version of the following: 1. R program 2. Program output: answers to each of the 5 questions Grade distribution: 15 points: function comments 10 points: R Console window (need to show that you compiled the function using the source command, and need to show that you called the function) 75 points: function output (print R Console screen; 15 points for the correct answer to each problem; print R Console screen).

Please i need full R program not only the out put i need the program line by line from the syntax to the out put.. thank you

Twenty years​ ago, 52​% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 209 of 700 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years​ ago? Use the alpha equals 0.1 level of significance. Click here to view the standard normal distribution table (page 1).LOADING... Click here to view the standard normal distribution table (page 2).LOADING... Because np 0 left parenthesis 1 minus p 0 right parenthesisequals 174.7 greater than ​10, the sample size is less than ​5% of the population​ size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied. ​(Round to one decimal place as​ needed.) What are the null and alternative​ hypotheses? Upper H 0​: p equals 0.52 versus Upper H 1​: p not equals 0.52 ​(Type integers or decimals. Do not​ round.) Determine the test​ statistic, z 0. z 0equals nothing ​(Round to two decimal places as​ needed.) Determine the critical​ value(s). Select the correct choice below and fill in the answer box to complete your choice. ​(Round to two decimal places as​ needed.) A. z Subscript alphaequals nothing B. plus or minusz Subscript alpha divided by 2equalsplus or minus nothing Choose the correct conclusion below. A. Reject the null hypothesis. There is insufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago. B. Do not reject the null hypothesis. There is sufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago. C. Do not reject the null hypothesis. There is insufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago. D. Reject the null hypothesis. There is sufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago.

Below is a table displaying the number of employees (x) and the profits per employee (y) for 16 publishing firms. Employees are recorded in 1000s of employees and profits per employee are recorded in $1000s.

What is the correlation between these two variables?

If a linear regression model were fit, what is the value of the slope and the value of the y-intercept?

In a test for the slope of the regression line being equal to zero versus the two-sided alternate, what is the value of the test statistic and the p-value?

A consultant for a large university studied the number of hours per week freshmen watch TV versus the number of hours seniors do. The result of this study follow. Is there enough evidence to show the mean number of hours per week freshman watch TV is different from the mean number of hours seniors do at alpha= 0.01?

For the Hypothesis stated above (in terms of Seniors- Freshmen)

What are the critical values?

What is the decision?

What is the p-value? (Round off to 4 decimal place)

You have five groups using different exercise techniques and you want to compare the average number of pounds lost. What test would be appropriate?

a. T-test

b. ANOVA

c. Person's correlation coefficient

d. Chi-square

A simple random sample from a population with a normal distribution of 100 body temperatures has a mean of 98.40 and s=0.68 degree F. Construct a 90% confidence interval.