Consider a refinery that produces three types of motor oil: Standard, Ex- tra, and Super. The selling prices are $9.00, $13.00, and $19.00 per barrel respectively. These oils can be made from three basic ingredients; crude oil, paraffin, and filler. The costs of the ingredients are $19.00, $9.00 and $11.00 per barrel, respectively. Company engineers have developed the following specifications for each oil Standard-60% paraffin, 40% filler Extra-at least 25% crude oil and no more than 45% paraffin Super-at least 50% crude oil and no more than 25% paraffin The CO2 emissions of Standard, Extra, and Super oils are 13.0, 11.8, and 8.0 units per barrel. With a supply capacity of 110, 90, and 70 thou- sand barrels per week for crude oil, paraffin, and filler, what should be blended in order to maximize profits as well as satisfy the requirements of the EPA to minimize the CO2 emissions from all the products of this industry? Solve the problem using the goal programming approach, if th goals are to have a profit greater than or equal to $5 per barrel and CO2 emissions less than or eaual to 10 units per barrel

How does lowering the screening cutoff point effect sensitivity and specificity, Positive predictive value, and Negative Predictive Value of the test assuming prevalence stays the same? Why?

You are a researcher who wants to know if there is a relationship between variable Y and variable X. You hypothesize that there will be a strong positive relationship between variable Y GPA and Variable X hours of sleep. After one semester, you select five students at random out of 200 students who have taken a survey and found that they do not get more than 5 hours of sleep per night. You select five more students at random from the same survey that indicates students getting at least seven hours of sleep per night. You want to see if there is a relationship between GPA and hours of sleep. Using a Pearson Product Correlation Coefficient statistic, determine the strength and direction of the relationship and determine if you can reject or fail to reject the HO:

Variable Y        Variable X    

2.5                      5               

3.4                      8                

2.0                      4               

2.3                     4.5              

1.6                     3     

3.2                     6

2.8                     7

3.5                     7.5

4.0                     6.5

3.8                     7

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 48 inches?

2. What is the probability that a randomly chosen 10 year old is between 50 and 51 inches?

3. If the shortest 10% 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 34 th percentile? inches

Using a random sample of n = 50, the sample mean is = 13.5. Suppose that the population standard deviation is σ=2.5.

Is the above statistical evidence sufficient to make the following claim μ ≠15:

?o: μ=15

??: μ ≠15

α = 0.05.

p value = 0

Interpret the results using the p value test.

Reject Ho

or

Do not reject Ho

Most married couples have two or three personality preferences in common. A random sample of 375 married couples found that 134 had three preferences in common. Another random sample of 573 couples showed that 215 had two personality preferences in common. Let p₁ be the population proportion of all married couples who have three personality preferences in common. Let p₂ be the population proportion of all married couples who have two personality preferences in common.

(a) Find a 90% confidence interval for p₁ – p₂. (Round your answers to three decimal places.)

Crimini mushrooms are more common than white mushrooms, and they contain a high amount of copper, which is an essential element according to the U.S. Food and Drug Administration. A study was conducted to determine whether the weight of a mushroom is linearly related to the amount of copper it contains. A random sample of crimini mushrooms was obtained, and the weight (x, in grams) and the total copper content (y, in mg) was measured for each. You may assume that all of the assumptions for regression are valid. Please include three decimal places in all answers.The work for all of the parts will be submitted at the end of the question. The summry data is given below:

n = 30 S_XX = 137.48 S_YY = 5.778 S_XY = 21.29 MSE = 0.0885 x̄ = 15.993

The line is

ŷ = -1.204 + 0.155 x

a) Find a 95% confidence interval for the true mean copper concentration when the weight of the mushroom is 18.2 g.

b)Find a 95% prediction interval for the true copper concentration when the weight of the mushroom is 18.2 g.

c) A value of 18.2 g is the size of an average Crimini mushroom. Is there any evidence to suggest that the you will get 1.9 mg of copper (the amount that is in one bar of dark chocolate) when you eat one average Crimini mushroom? Be sure to mention which interval, from above.

Ten observations were selected from each of 3 populations and an analysis of variance was performed on the data. The following are the results:

A. Using alpha= .05, test to see if there is a significant difference among the means of the three populations.

B. If in part A you concluded that at least one mean is different from the others, determine which mean is different using LSD method. The three samples are (mean) X1=24.8, X2=23.4, X3=27.4.

According to a study conducted for Gateway Computers, 59% of men and 70% of women say that weight is an extremely/very important factor in purchasing a laptop computer. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly higher proportion of women than men believe that weight is an extremely/very important factor in purchasing a laptop computer? Use alpha= 0.05.

Write the correct R commands for solving this problem. What is the p value? What is the statistical decision?

Use R command to construct a 90% confidence interval to estimate the difference in proportion of women and men believe that weight is an extremely/very important factor in purchasing a laptop computer.

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester.

In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 36 expectant mothers have mean weight increase of 16.1 pounds in the second trimester, with a standard deviation of 6.1 pounds.

A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds.

Find the $p$-value for the hypothesis test.

The $p$-value should be rounded to 4 decimal places.

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 495 eggs in group I boxes, of which a field count showed about 268 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 784 eggs in group II boxes, of which a field count showed about 272 hatched.

(a) Find a point estimate p̂₁ for p₁, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.)
p̂₁ =  

Find a 95% confidence interval for p₁. (Round your answers to three decimal places.)

(b) Find a point estimate p̂₂ for p₂, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.)
p̂₂ =  

Find a 95% confidence interval for p₂. (Round your answers to three decimal places.)

(c) Find a 95% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

The following data were obtained from a repeated-measures study comparing 3 treatment conditions. Use a repeated-measures ANOVA with a=.05 to determine whether there are significant mean differences among the three treatments (do all 4 steps of conducting a hypothesis test!!):

A measure of the strength of the linear relationship that exists between two variables is called: Slope/Intercept/Correlation coefficient/Regression equation. If both variables X and Y increase simultaneously, then the coefficient of correlation will be: Positive/Negative/Zero/One. If the points on the scatter diagram indicate that as one variable increases the other variable tends to decrease the value of r will be: Perfect positive/Perfect negative/Negative/Zero. The range of correlation coefficient is: -1 to +1/0 to 1/-∞ to +∞/0 to ∞. Which of the following values could NOT represent a correlation coefficient? r = 0.99/r = 1.09/r = -0.73/r = -1.0. The correlation coefficient is used to determine: A specific value of the y-variable given a specific value of the x-variable/A specific value of the x-variable given a specific value of the y-variable/The strength of the relationship between the x and y variables/None of these. If two variables, x and y, have a very strong linear relationship, then: There is evidence that x causes a change in y/There is evidence that y causes a change in x/There might not be any causal relationship between x and y/None of these alternatives is correct. If the Pearson correlation coefficient R is equal to 1 (r=1) then: There is a negative relationship between the two variables. /There is no relationship between the two variables. /There is a perfect positive relationship between the two variables. /There is a positive relationship between the two variables. If the correlation between 2 variables is -.77, which of the following is true? There is a fairly strong negative linear relationship/An increase in one variable will cause the other variable to decline by 75%

a random sample of 175 xray machines is taken. and 54 machines in the sample malfunction. compute a 95% confidence interval for the proportion of all xray machines that malfunction. then calculate the upper and lower limit of the 95% confidence intervals

In a recent marketing campaign, Olive Garden Italian Restaurant® offered a “NeverEnding Pasta Bowl.” The customer could order an array of pasta dishes, selecting from 7 types of pasta and 6 types of sauce, including 2 with meat.

a. If the customer selects one pasta type and one sauce type, how many “pasta bowls” can the customer order?

b. How many different “pasta bowls” can the customer order without meat?