# Assistance with Statistics Homework

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Question description

1.  A large school district is reevaluating its teachers' salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The researcher uses years of experience to predict salary. The raw data is given in the table below.

 Salary Yrs Exp \$23,250.00 7.5 \$22,195.00 2 \$37,800.00 14.5 \$42,250.00 15 \$42,000.00 17 \$18,055.00 1

SHOW WORK:

a. The estimated regression equation is ________.

b. Using Excel (attach output), the correlation coefficient is ____. Interpret this value.

c. Using Excel, the coefficient of determination is _____.  Interpret this value.

d. Is there a linear relationship between a teacher's salary and their years of experience.  Use a 0.05 level of significance. Explain.

2.  Katherine D’Ann is planning to finance her college education by selling the programs at the football games for State University. There is a fixed cost of \$360 for printing these programs and the variable cost is \$3.50. There is also a \$800 fee that is paid to the university for the right to sell these programs. If Katherine was able to sell the programs for \$4.85 each, how many programs would she have to sell in order to break even?

SHOW WORK

3.  Steve Goodman, production foreman for the Florida Gold Fruit Company, estimates that the average sale for oranges is 4,600 and the standard deviation is 450 oranges.  Sales follow a normal distribution.

Don't forget to draw your graphs and show the formulas used.

a.  What is the probability that the sales will be less than 5,750 oranges?

b.  What is the probability that the sales will be between 3,300 and 4, 900 oranges?

c.  What is the probability that the sales will exceed 5400 oranges?

4.  A market study taken at a local sporting goods store showed that of 20 people questioned, 8 owned tents, 9 owned sleeping bags, 7 owned camping stoves, 5 owned both tents and camping stoves, 6 owned both tents and sleeping bags, and 3 owned both sleeping bags and camping stoves.

 Let: Event A = owns a tent Event B = owns a sleeping bag Event C = owns a camping stove

Don't forget to show all formulas used.

a. Find P(A),  P(B) and P(C).

b.  If a person owns a camping stove, what is the probability they also own a tent?

c. What is P (A ∩ B)?

d. Are events B and C mututally exclusive? Are events B and C independent? Explain.

5. An appliance dealer must decide how many (if any) new microwave ovens to order for next month. The ovens cost \$220 and sell for \$300. Because the oven company is coming out with a new product line in two months, any ovens not sold next month will have to be sold at the dealer's half price clearance sale.  Additionally, the appliance dealer feels he suffers a loss of \$25 for every oven demanded when he is out of stock. On the basis of past months' sales data, the dealer estimates the probabilities of monthly demand (D) for 0, 1, 2, or 3 ovens to be .35, .4, .15, and .1, respectively.

Note:

-Decision alternative (Whether the dealer should buy (order)  0, 1, 2 or 3 ovens??)

-States of Nature (The demand by customers of 0, 1, 2 or 3 ovens)

-This is a profit table.

- Assume that the unsold ovens will be purchased at the clearance sale.  So. instead of the

dealer losing the entire \$220 on an unsold oven, they will only  lose \$70 (220-150).

 Demand For Ovens Ovens Ordered 0 1 2 3 0 0 −25 −50 -75 1 −70 80 55 30 2 −140 10 160 135 3 -210 −60 90 240

What is the best decision, if the dealer uses

a.  the minmax regret approach,

b.  the conservative approach,

c.  the optimistic approach.

d.  How much should this dealer be willing to pay to have perfect information regarding the demand of the ovens? Explain.

6. Fast Service Store has maintained daily sales records on the various size "Cool Drink" sales.

 "Cool Drink" Price Number Sold \$0.25 65 \$0.75 100 \$0.95 ? \$1.10 ? Total 380

From past data, let's say the we were able to determine that the average (expected value) daily sales price for a "Cool Drink" is 0.82.  Assuming that past performance is a good indicator of future sales,

a.  the probability of a customer purchasing a \$0.95 "Cool Drink?" is  ______.

b.  the probability of a customer purchasing a \$1.10 "Cool Drink?" is ________.

C.  the probability of a customer purchasing a "Cool Drink" that costs \$0.75 or less is ______.

d.  the variance of a "Cool Drink" is ______.

If you had trouble with finding the probabilitities for (a) or (b), simply make up two probabilities and use those values to compute the variance.

USE THREE OR MORE DECIMAL PLACES FOR EVERY STEP AND PART OF THIS PROBLEM!

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