La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a rose wine, and fruit juice. To meet taste specifications, the wine cooler must consist of at least 50% white wine, at least 20% and no more than 30% rose, and exactly 20% fruit juice. La Jolla purchases the wine from local wineries and the fruit juice from a processing plant in San Francisco. For the current production period, 10000 gallons of white wine and 8000 gallons of rose wine can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the wine are $1 per gallon for the white and $1.5 per gallon for the rose; the fruit juice can be purchased for $0.5 per gallon. La Jolla Beverage Products can sell all of the wine cooler it can produce for $2.5 per gallon.

a. Is the cost of the wine and fruit juice a sunk cost or a relevant cost in this situation? Explain.

b. Formulate a linear program to determine the blend of the three ingredients that will maximize the total profit contribution. Solve the linear program to determine the number of gallons of each ingredient La Jolla should purchase and the total profit contribution it will realize from this blend. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

Profit Contribution = __________

c. If La Jolla could obtain additional amounts of the white wine, should it do so? YES OR NO

If so, how much should it be willing to pay for each additional gallon, and how many additional gallons would it want to purchase?

d. If La Jolla Beverage Products could obtain additional amounts of the rosé wine, should it do so? YES OR NO.

If so, how much should it be willing to pay for each additional gallon, and how many additional gallons would it want to purchase?

e. Interpret the shadow price for the constraint corresponding to the requirement that the wine cooler must contain at least 50% white wine. What is your advice to management given this shadow price?

f. Interpret the shadow price for the constraint corresponding to the requirement that the wine cooler must contain exactly 20% fruit juice. What is your advice to management given this shadow price?

1. An impartial judge of a local garden competition collects scores from two groups of judges on what he suspects to be the number one garden. He finds the first group (n = 5) has a mean score of 76. The second group (n = 3) has a mean score of 91. So that he may declare the final score, what is the weighted mean of these two groups?

2. A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online. Student Score Student Score A 94 F 96 B 88 G 25 C 74 H 61 D 88 I 82 E 98 J 98

(a) What is the range of data in this population? min

(b) What is the IQR of data in this population? min

(c) What is the SIQR of data in this population? min

(d) What is the population variance?

(e) What is the population standard deviation? (Round your answer to two decimal places.) min

3. A sociologist records the annual household income (in thousands of dollars) among a sample of families living in a high-crime neighborhood. Locate the lower, median, and upper quartiles for the times listed below. Hint: First arrange the data in numerical order.

a) lower quartile thousand dollars

b) median thousand dollars

c) upper quartile thousand dollars

42 22 46 33 37 32 37 47 51 25

4. A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction. Age 13–16 Time Age 17–21 Time 1 10 1 4 2 9 2 3 3 3 3 7 4 1 4 4 5 10 5 8 6 3 6 1 7 8 7 2 8 9 8 5 9 6 9 4 10 5 10 2 Using the computational formula, for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.) what is the

a) SS

b) sample variance

c) standard deviation

4 [20% ]

(a) Prove the Sine Rule for a spherical triangle: [10%] sin α sin a = sin β sin b = sin γ sin c

(b) Show that the area of a spherical triangle on the unit sphere is [10%] α + β + γ − π .

We consider a population of cars from a given model year. A sample of 24 such cars

has been recently sold. The sale price as a function of the age of the car is in the Excel

file S4.XLSX (Car) in the Excel directory.

a. Try a linear regression and an exponential (non-linear) regression with Excel to

fit these data. Comment your results.

b. Which regression model seems to fit the data better and why?

c. Run the LINEST function in Excel. Provide the result table.

Suppose we want to know how registered voters in Kane County feel about the 2016 presidential election. Specifically, we’d like to get an overall summary, but be sure we have a representative sample of registered Democrats, Republicans, and those with no political party affiliation or a party other than Democrat or Republican. Why would a stratified sample be appropriate, and how would we determine how many of each party to sample if we wanted to survey 200 total voters? Shown below are the total as of August 13, 2019.

1a)Out of the 50 candidates in the question above, 28 are women and 22 are
men. How many ways can the committee of 12 be randomly chosen where 7 members
are women and 5 members are men?

b) In a group of students, each student is taking a mathematics course or a
computer science course or both. One-fifth of those taking a mathematics course are
also taking a computer science course, and one-sixth of those taking a computer science
course are also taking a mathematics course. What percentage of the students
are taking a mathematics course?

c) A coin is flipped 10 times. How many outcomes have exactly 3 heads?

d) Three committees of 5, 10, and 15 are to be chosen out of a total of 30. How
many ways can the committee be formed?

Use the following information to answer the first 5 questions:

Suppose we wanted to estimate the average age of a certain group of divorced men during 1988 and took a random sample of (n = ) 100 giving us x =35.2 years old.

1. this is the symbol that represents the average age of the population
2. this is the amount of people in the sample
3. this is the average age found from our sample
4. this is the symbol we use to represent the average age of the sample
5. this is the population

Answer choices

(a) 35.2 (b) 100

(c) m (d) x

(e) the average age of a certain group of divorced men during 1988

Suppose we wanted to estimate the average age of a certain group of divorced men during 1988 and took a random sample of n = 7 and received the following ages: 37, 22, 31, 43, 39, 61, and 26.

6) Calculate . You can use a Google Spreadsheet if you’d like since you should know by now how to calculate averages this way. We will learn another way soon (which most of you know at this time from previous courses).

x = 37 years old Answer choices: (a) True (b) False

Use the following information to answer the next three questions and choose the best answer::

To determine the average height of Cornell University males, two Sociology students sampled 50 males, yielding an average height of 5’10”.

7) What is the population parameter of interest?

(a) two Sociology students

(b) 50 males

(c) the average height of Cornell University males

8) What is the sample?

(a) two Sociology students

(b) 50 males

(c) the average height of Cornell University males

9) What symbol would we use to represent the average height of 5’10” ?

(a) n

(b) x

(c) m

Decide if the following statements are descriptive or inferential.

10) About 85% of women in the US have a job.  

11) The mean grade on the MA 161 final given last semester was an 83.

12) Drinking bubble tea can raise cholesterol levels by 10%.  

Answer choices: (a) Descriptive (b) Inferential

Decide if the following statements are quantitative or categorical (if categorical whether they are binary)

13) The age of a groom on his wedding day.

14) Whether a spun penny lands on heads or tails.

Answer choices:

(a) Quantitative

(b) Categorical - not binary    

(c) Categorical - binary

15) Any x found is a parameter Answer choices: (a) True (b) False

A researcher was interested in utilities provided by city governments. The researcher randomly selected 20 counties from a list of all counties in the U.S. From each of these counties the researcher then contacted each city government (a total of 192) and found that 12 (6.25%) of them provided electricity to their residents. In this situation the sampling frame is

Select one:

a. the list of all counties in the U.S.

b. the 316 cities.

c. the 20 counties.

d. 6.25%.

Why is variation in a candidate measure within population important to assessing the measure validity?

A travel photographer visits 10 paradise locations (N = 10) and rates each sequentially. 7, 5, 8, 5, 1, 9, 8, 11, 7, and 6 Using the computational formula, what is the SS and σ2? SS = σ2 =

How would fast-food workers introduce bias into the manager's sample of drive-thru times?

1.  You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ=26.2σ=26.2 dollars. You would like to be 99% confident that your estimate is within 2 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

2. You measure 27 watermelons' weights, and find they have a mean weight of 30 ounces. Assume the population standard deviation is 7.4 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.

Give your answer as a decimal, to two places

3.

Statistics students in Oxnard College sampled 11 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The bivariate data are shown below:

A student calculates a linear model
yy =  xx + . (Please show your answers to two decimal places)
Use the model to estimate the cost when number of pages is 949.
Cost = $ (Please show your answer to 2 decimal places.)

4.

Statistics students in Oxnard College sampled 11 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The data are shown below:

A student calculates a linear model using technology (TI calculator)
ˆyy^ =  xx + . (Please show your answers to two decimal places)
Use the model to estimate the cost when number of pages is 574.
Cost = $ (Please show your answer to 2 decimal places.)

For MSE (mean square error), why is it important to to know the parameters of the distribution of the sample values of the attributes used for the observations ? please provide example and a thorough explanation. Please explain why we need to know the parameter to calculate MSE

1. You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 95% confident that you estimate is within 3% of the true population proportion. How large of a sample size is required?

2. A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 8% margin of error at a 90% confidence level, what size of sample is needed

3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=45.1σ=45.1. You would like to be 98% confident that your estimate is within 4 of the true population mean. How large of a sample size is required?

4. You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ=51.3σ=51.3 dollars. You would like to be 95% confident that your estimate is within 1.5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?