Consider the following linear program, which maximizes daily total profit for two products, regular (R), and super (S):

MAX Z = 50R + 75S

s.t.

1.2R + 1.6 S ≤ 600 assembly (hours)

0.8R + 0.5 S ≤ 300 paint (hours)

.16R + 0.4 S ≤ 100 inspection (hours)

R, S ≥ 0

Implement the LP problem in a spreadsheet model and invoke Solver to obtain the optimal solution. Use label and formatting to enhance readability of model and Solver reports.

1. Create spreadsheet model

<Paste screenshot of spreadsheet model>

2. Invoke Solver to find optimal solution

<Paste screenshot of Answer Report>

            <Paste screenshot of Sensitivity Report>

3. What is the optimal solution?
4. What is the maximum daily profit?
5. What resources are binding at optimality?

For questions 15-20, consider a box with 3 red and 5 blue balls. 15. If one ball is drawn at random, what is the probability that the color is red? The probability that you pick a red ball is 3/8. 3 red, 5 blue 3+5=8 Therefore, 3/8. https://canvas.park.edu/files/5516027/download?download_frd=1&verifier=6xdC2s8YTdrrfONH1TZPJUK9jRKzh2UmtaqIbg9y 16. If two balls are drawn at random, what is the probability that both are red? Utilizing the tree... P (R X R)=(3/8) (2/7) 17. Two balls are drawn at random. If it is known that the first one is red, then what is the probability that the second one is red? 18. If two balls are drawn at random, what is the probability that they have the same color? 19. If two balls are drawn at random, what is the probability that they have different colors? 20. If three balls are drawn at random, what is the probability that at least one of them is blue?

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the value of the F statistic for blocks?

Each sweat shop worker at a computer factory can put together 4.5 computers per hour on average with a standard deviation of 0.8 computers. 8 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4.6 and 4.7 computers per hour.
5. For the 8 workers, find the probability that their average number of computers put together per hour is between 4.6 and 4.7.
6. Find the probability that a 8 person shift will put together between 33.6 and 36.8 computers per hour.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. A sticker that says "Great Dedication" will be given to the groups of 8 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

#14

Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(f) Make a summary table for your ANOVA test.

1.  Find the margin of error for the mean weight of medium Antonio’s cheese pizza if a sample of size n = 16 produces a sample standard deviation of 4.220 g, assuming 95% confidence. Round to two decimals.

2. The mean and standard deviation for voltages of power packs labeled as 12 volts for a sample of 25 are as follows:

Please develop a 95.00% confidence interval for the sample above. (Round to 3 decimal places.)
Lower limit = ?

Upper limit = ?

3. The actual voltages of power packs labeled as 12 volts for a sample are as follows: 11.90, 11.79, 11.38, 11.79, 12.21, 11.95, 11.38, 11.01.
Please develop a 90.00% confidence interval for the sample above.

Lower limit = ?

Upper limit = ?

4. Assuming the random variable X is normally distributed, compute the lower and upper limits of the 90% confidence interval for the population mean if a random sample of size n=7 produces a sample mean of 12 and sample standard deviation of 6.00. Round to two decimals.

Lower Limit = ?,

Upper Limit = ?

5. A random sample of 22 scalpers’ ticket prices for a rock concert has sample mean $44.00 and sample standard deviation of $6.02. What is the upper and lower limit of the 95% confidence interval of mean scalpers’ ticket prices? Round to two decimals.

Lower Limit = ?

Upper Limit = ?

Please state whether effect measure modification, confounding, neither or both is present in each scenario.

1. In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans stated that a candidate’s positions on the issue of family values are extremely or very important in determining their vote for president.
2. Obtain a point estimate for the proportion of adult Americans for which the issue of family values is extremely or very important in determining their vote for president.
3. Verify that the requirements for constructing a confidence interval for p are satisfied
4. Construct 90%, 95% and 99% confidence intervals for the proportion of adult Americans for which the issue of family values is extremely or very important in determining their vote for president. Be sure to give a proper interpretation of each interval
5. What do you notice about the width of each confidence interval as the confidence level increases?

A research team is studying a new pain medication for patients suffering from fibromyalgia. Patients suffering from chronic pain as a result of fibromyalgia were divided into two categories: Treatment and Placebo. Patients in the treatment group were injected with the new drug while patients in the placebo group were injected with saline solution. Neither the patients, nor the health care practitioners admininstering the study knew who was receiving the actual drug.

After two weeks the patients were asked to pick which category (1-10) their pain abatement fit into, where 1 meant they were no longer in pain, while 10 meant they had no change.

1.) Based on the experimental design of this study and the kind of data generated, which statistical test should be used to determine if pain relief was independent of treatment group?

Researchers want to survey the mass of American alligators in a certain region. They want to maximize the efficiency of this effort, and get as many measurements as possible. Capturing alligators, putting them on a scale, and releasing them involves risk and time and subjects the animals to stress. They decide to survey alligators from the air. In this manner they can measure the length of the animals. They want to use these measurements to estimate the mass of the alligators. They have access to data about length and mass of captive alligators that they want to use to predict the mass of wild alligators.

2.) Which of the following best describes the alternate hypothesis for a t-test on the slope of the line relating alligator length and weight?

Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ μ = 130 mg/dl and σ σ = 15 mg/dl. (a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes? (b) If measurements are made on 5 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

please show me your process . Thank you

1. The following table provides data for 20 samples each of size five.

1. Identify out-of-control points. If necessary, recompute the control limits after removing the outliers. What do you conclude? (10 pts) Please answer in detail using excel

Test the following hypotheses and interpret your findings.

Joan moves into her new apartment and wants to purchase a new couch. She wants to determine if the average cost of couches at Store 1 is cheaper than Store 2. At Store 1 the average cost of 20 couches is $650 with a standard deviation of $61. At Store 2 the average cost of 22 couches is $730 with a standard deviation of $78. At alpha = .05, what are the results if you want to determine that Store 1 is cheaper than Store 2 in couch prices? Accept H0, the test statistic is greater than -2.021. Reject H0 the test statistic is less than -2.021. Accept H0 the test statistic is greater than -1.684. Reject H0 the test statistic is less than -1.684.

The mean number of close friends for the population of people living in the U.S. is 5.7. An investigator predicts that the mean number of close friends for introverts will be significantly different than the mean of the population. The mean number of close friends for a sample of 26 introverts is 6.5. The standard deviation of scores in this sample is 1.3. Do these data support the investigator's prediction?

a. State the null and alternative hypotheses in symbolic form.

b. Set the criteria for making a decision. What are the critical values? 
(Use a = .01) 


c. Compute the appropriate test statistic. Show your work.

d. Based on your results, evaluate the null hypothesis. Circle One: Reject H0 e. State your conclusions in terms of the original research.

f. Compute Cohen’s d and interpret the effect (i.e., is it a small, medium, or large effect) g. Compute the 99% confidence interval for this study

Fail to Reject H0

Interpret the 99% confidence interval below.
We can be _______________________________________________________________ that, over repeated sampling, the

interval between____________________________________ and _________________________________________

contains the true population mean in _________________________________________________________ for

________________________________________________________________________________________________.

PLEASE BE VERY SPECIFIC AND SHOW EVERY SINGLE STEP IN DETAIL, SPECIALLY IF USING R PROGRAM. (I NEED MORE HELP WITH PART D AND E!!!)

A bottling company uses a machine to fill bottles with a tasty beverage. The bottles are advertised to contain 300 milliliters (ml), but in reality the amount varies according to a normal distribution with mean μ=298ml and standard deviation σ=3 ml. (For this problem, we’ll assume σσ is known and carry out the calculations accordingly).

a)What is the probability that a randomly chosen bottle contains less than 296 ml?

b)Given a simple random sample of size n=6 bottles, what is the probability that the sample mean is less than 296 ml?

c)What is the probability that a single bottle is filled within 11 ml of the true mean μ=298ml? Hint: Draw the distribution and shade in what probability you want… then convert that to a question about standard normals. To find the answer using a table or R, you need to look up two values and perform a subtraction.

d)What is the probability that the mean of 10 randomly selected bottles is within 11 ml of the mean? What about the mean of a sample of n=100 bottles?

e)If a sample of size n=50 has a sample mean of ¯x=298, should this be evidence that the filling machine is out of calibration? i.e., assuming the machine has a mean fill amount of μ=300 and σ=3, what is P(¯X≤298)?