MPG
36.3
41
36.9
37.1
44.9
36.8
30
37.2
42.1
36.7
32.7
37.3
41.2
36.6
32.9
36.5
33.2
37.4
37.5
33.6

1. The EPA collects data on 20 cars and calculates their gas mileage in miles per gallon (MPG).

d) Using the modified box-plot methodology determine if there are any outliers and justify. You do not have to make the box-plot!

e) Create a new variable by subtracting the mean from each observation and then dividing the difference by the standard deviation.

f) Find the mean, median and standard deviation of the new variable.

g) In one or two sentences, describe the original data.

What is the equation for the weighted least square solution for a non-linear problem? Which two conditions are satisfied when using the method of least squares?

A Student is trying to calculate their final grade. The student estimates the their performance on the following table.

You must complete the table to receive any marks. (Use at least five decimals when necessary)

(a)  What is the expected grade?

answer:

(b)  What is the standard deviation of expected grade?

answer:

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(c)  If a student expects to earn an additional $ 16.5 per year for each % point they scored on their final grade, and there was a cost of $ 400 for school fees, plus $ 650 for tuition. What is the expected profit from this course in their first year of work?

answer:

An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table (to 2 decimals, if necessary and p-value to 4 decimals).

Use "a" = .05 to test for any significant differences.

What is the p-value?

Confidence Intervals – Means & Proportions

1.    You would like to estimate the starting salaries of recently graduated business majors (B.S. in any business degree). You randomly select 60 recently graduated business majors and get a sample mean of $43,800 and the population standard deviation is known to be $8,198

A.    Construct a 90% confidence interval to estimate the average starting salary of a recently graduated business major (Round to the nearest penny and state the answer as an interval – for example $351.89 to $728.14).

B.    Using the same confidence level, you would like the margin of error to be within $500, how many recently graduated business majors should you sample?

1. The following 10 numbers were drawn from a population. Is it likely that these numbers came from a population with a mean of 13? Evaluate with a two-tailed test at p < .05.

5, 7, 7, 10, 10, 10, 11, 12, 12, 13

a. State both in words, and then symbolically what your H1 and H0 would be.

b. What is your df? What is your critical t?

c. Calculate t

d. Based on the above information, would you reject H0, or fail to reject it? Why? How would you state your conclusion in words?

e. Bonus Credit: Calculate the 95% confidence interval for the alternative hypothesis distribution.

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:

The credit union will have $1.9 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:

• Risk-free securities may not exceed 35% of the total funds available for investment.

• Signature loans may not exceed 12% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).

• Furniture loans plus other secured loans may not exceed the automobile loans.

• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $1.9 million be allocated to each of the loan/investment alternatives to maximize total annual return?

What is the projected total annual return?

Annual Return = $

Please show all work thank you!

When testing for a disease such as the flu, there is always the possibility of receiving a false negative (meaning that you have the disease but tested negative) and a false positive (meaning that you do not have the disease but tested positive).

Last month, a collection of people at a clinic were tested for the flu. After the results were confirmed after medication, here were the results.

1. 1) How many people were used in this study?

2. 2) What is the probability that someone at this clinic tested positive for the flu and actually had the flu?

3. 3) What is the probability that someone at this clinic tested negative for the flu and actually did not have the flu?

4. 4) What is the probability that someone tested at this clinic got a test result that was correct?

5. 5) What is the probability that someone tested at this clinic got an incorrect test result?

6. 6) What is the probability that a false positive was obtained? (Hint: This is the probability that someone tested positive, given that they actually did not have the flu).

7. 7) What is the probability that a false negative was obtained? (Hint: This is the probability that someone tested negative, given that they actually did have the flu).

8. 8) Looking at the rates in #5, 6, and 7, do you feel that this clinic’s error rate is too high? Support your answer with your thinking on this. (An answer of ‘yes’ or ‘no’ only will notreceive credit).

For each of the following uncertain quantities, discuss whether it is reasonable to assume that the probability distribution of the quantity is binomial. If you think it is, what are the parameters n and p? If you think it isn’t, explain your reasoning.

a. The number of wins the Boston Red Sox baseball team has next year in its 81 home games

b. The number of free throws Kobe Bryant misses in his next 250 attempts

c. The number of free throws it takes Kobe Bryant to achieve 100 successes

d. The number out of 1000 randomly selected customers in a supermarket who have a bill of at least $150

e. The number of trading days in a typical year where Microsoft’s stock price increases

f. The number of spades you get in a 13-card hand from a well-shuffled 52-card deck

g. The number of adjacent 15-minute segments during a typical Friday where at least 10 customers enter a McDonald’s restaurant

h. The number of pages in a 500-page book with at least one misprint on the page.

You plan to invest​ $1,000 in a corporate bond fund or in a common stock fund. The table presents the annual return​ (per $1,000) of each of these investments under different economic conditions and the probability that each of these economic conditions will occur.

Probability   Economic_Condition   Corporate_Bond_Fund   Common_Stock_Fund
0.01   Extreme_recession -250 -999
0.09   Recession -60 -300
0.20   Stagnation 30 -150
0.30   Slow_growth 80   70
0.35   Moderate_growth 120 200
0.05   High_growth 150 350

Calculate the expected return for the corporate bond fund and for the common stock fund.

The expected return for the corporate bond fund is

​(Round to the nearest cent as​ needed.)

The expected return for the common stock fund is

​(Round to the nearest cent as​ needed.)

Calculate the standard deviation for the corporate bond fund and for the common stock fund.

The standard deviation for the corporate bond fund is

​(Round to the nearest cent as​ needed.)

The standard deviation for the common stock fund is

​(Round to the nearest cent as​ needed.)

If an investor chooses to invest in the common stock fund in​ (c), what should the investor think about the possibility of losing ​$980 of every​ $1,000 invested if there is an extreme​ recession?

A.The investor would need to assess on how to respond to the almost certainty that almost all of the investment could be lost.

B.The investor would need to assess on how to respond to the small possibility that almost all of the investment could be lost.

C.The investor would need to assess on how to respond to the small possibility that about​ 10% of the investment could be lost.

D.The investor would need to assess on how to respond to the almost certainty that about​ 10% of the investment could be lost.

1. The correlation coefficient is

1. a unitless measure of the strength of the linear relationship between two quantitative variables
2. a unitless measure of the strength of the linear relationship between two categorical variables
3. measured in the same units as the larger quantitative variable
4. measured in the same units as the smaller quantitative variable

2. A random sample of 15 weeks of sales (measured in $) and 15 weeks of advertising expenses (measured in $) was taken and the sample correlation coefficient was found to be r = 0.80.  Based on this sample correlation coefficient we could state

1. That the percentage of the variation in sales that is shared with the variation in advertising is about 80%.
2. That the percentage of the variation in sales that is shared with the variation in advertising is about 64%.
3. That the percentage of variation that is shared by the two variables cannot be determined from the information given.
4. That the percentage of variation that is shared between the two variables is 100% because the two variables are positively correlated.

3. A scatterplot of two variables is constructed.  “Stretching” the scatterplot horizontally or vertically would

1. Change the perceived slope but not the correlation.
2. Change the correlation but not the perceived slope
3. Leave the correlation and the perceived slope unchanged.
4. Change both the correlation and the perceived slope.

4. A random sample of 40 students commuting to campus by bicycle is taken.  The correlation between the time spent waiting at traffic lights and total cycling time was r = 0.6.  This means:

1. The average rider spent sixty percent of their total cycling time to campus waiting at traffic lights.
2. The more time a rider spends waiting at traffic lights, the higher their total time commuting time is likely to be.
3. If the rider's time at traffic lights increases by 6 minutes, then they will spend an additional 12 minutes commuting to campus by bicycle, on the average.
4. If the rider's time at traffic lights increases by 12 minutes, then they will spend an additional 6 minutes commuting by bicycle, on the average.

1. Hayes Electronics stocks and sells a particular brand of personal computer. It costs the firm $450 each time it places an order with the manufacturer for the personal computers. The cost of carrying one PC in inventory for a year is $170. The store manager estimates that total annual demand for the computers will be 1,200 units, with a constant demand rate throughout the year. Orders are received within minutes after placement from a local warehouse maintained by the manufacturer. The store policy is never to have stockouts of the PCs. The store is open for business every day of the year except Christmas Day. Determine the following:

   1. The optimal order quantity per order

   2. The minimum total annual inventory costs

   3. The optimal number of orders per year

   4. The optimal time between orders (in working days)

2. Hayes Electronics in Problem 1 assumed with certainty that the ordering cost is $450 per order and the inventory carrying cost is $170 per unit per year. However, the inventory model parameters are frequently only estimates that are subject to some degree of uncertainty. Consider four cases of variation in the model parameters: (a) Both ordering cost and carrying cost are 10% less than originally estimated, (b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is 10% higher and carrying cost is 10% lower than originally estimated, and (d) ordering cost is 10% lower and carrying cost is 10% higher than originally estimated. Determine the optimal order quantity and total inventory cost for each of the four cases. Prepare a table with values from all four cases and compare the sensitivity of the model solution to changes in parameter values.

I need the answer for question 2.

Optimized Cookie Production for a BCS Party. A friend was bringing small bags of cookies to sell at a fairly large BCS Championship Game Watch Party (there were no TCU fans present, however). Three kinds of cookies were sold: Stars (sold for $1 per bag), Circles (sold for $0.75 per bag), and Stars and Stripes (sold for $1.50 per bag). He was to bring the cookies to the Watch Party in three large boxes. (The boxes did not have to be full, but he could not bring more than three large boxes of cookies). By volume, it is a known fact that one of the large boxes can hold 100 bags of Stars, 120 bags of Circles, or 80 bags of Stars and Stripes (or a corresponding mix of cookies). HINT: Don’t concern yourself with what each box held; view this as an aggregate limit in the numbers of cookies. Previous parties had given him some hints on the demand for cookies – he knew that for the sake of variety, he needed to make at least 45 bags of each type of cookie. As he was planning his cookie composition, he also realized he was constrained by time in putting together the cookie bags. Circle cookies and Stars cookies took 1 minute per bag to finish; because Stars and Stripes had more icing, it took 2 minutes to finish each bag. He allocated 420 minutes (7 hours) to put the bags together. Can you determine how many of each of the three cookie types your friend should make to maximize sales (a surrogate for profit)?

A survey of 547 Americans was asked if commuting to work was stressful. 24% of them said that it was. Find a 95% confidence interval for the proportion of American that find commuting to work stressful.