Kuantan ATV, Inc. assembles five different models of all-terrain vehicles (ATVs) from various ready-made components to serve the Las Vegas, Nevada, market. The company uses the same engine for all its ATVs. The purchasing manager, Ms. Jane Kim, needs to choose a supplier for engines for the coming year. Due to the size of the warehouse and other administrative restrictions, she must order the engines in lot sizes of 1,000 each. The unique characteristics of the standardized engine require special tooling to be used during the manufacturing process. Kuantan ATV agrees to reimburse the supplier for the tooling. This is a critical purchase, since late delivery of engines would disrupt production and cause 50 percent lost sales and 50 percent back orders of the ATVs. Jane has obtained quotes from two reliable suppliers but needs to know which supplier is more cost-effective. The terms of sale are 5/10 net 30 for Supplier 1 and 3/10 net 30 for Supplier 2. The data related to the costs of ownership associated with two reliable suppliers has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Questions

1. What is the total cost of ownership for each of the suppliers? Assume the buyer will take advantage of the largest discount. Do not round intermediate calculations. Round your answers to the nearest cent.

2. Which supplier is more cost-effective?

The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values. If meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins (b) x=10 wins (c) x=21 wins (d) x=15 wins

The equation of the regression line is y= ? x+? (Round to two decimal places as needed.)

a. Predict the ERA for 5 wins, if it is meaningful.Select the correct choice below and ,if necessary, fill in the answer box within your choice.

A. ^y= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=5 is well outside the range of the original data.

C. It is not meaningful to predict this value of y because x=5 is not an x-value in the original data.

(b) Predict the ERA for 10 wins, if it is meaningful.Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=10 is not an x-value in the original data.

C. it is not meaningful to predict this value of y because x=10 is inside the range of the orginal data.

(c) Predict the ERA for 21 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your

choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=21 is not x-value in the original data.

C. it is not meaningful to predict this value of y because x=21 is well outside the range of the original data.

(d) Predict the ERA for 15 wins, if it meaningful. Select the correct choice below and,if necessary,fill in the box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=15 is inside the range of the original data.

C. It is not meaningful to predict this value of y because x=15 is not an x-value in the original data.

Wins, x Earned run average, y

20, 2.82

18, 3.24

17, 2.56

16, 3.65

14, 3.79

12, 4.34

11, 3.78

9, 5.07

Moonbucks roasts 2 types of coffee: Guatemala Gold and Sumatra Silver. Each month, the demand for each coffee type is uncertain. For Guatemala Gold, the mean demand is 20,000 pounds and the standard deviation is 5,000 pounds. For Sumatra Silver, the mean demand is 10,000 pounds and the standard deviation is 5,000 pounds. The demand for Guatemala Gold and Sumatra Silver is negatively correlated with a correlation of −0.4, since some customers tend to buy whichever coffee is
on sale that month. It takes time to roast each type of coffee, and both coffees are roasted on the Clover Roasting Machine. The Clover Machine can process 125 pounds of Guatemala Gold per hour, but only 50 pounds of Sumatra Silver per hour. Although the Clover Machine can only roast one of the two coffees at any given moment, it is simple to switch between roasting Guatemala Gold and Sumatra Silver, so there is no setup time required in addition to the roasting times mentioned above.
a. What is the covariance of the demand for Guatemala Gold and the demand for Sumatra Silver?
b. First express T (total roasting time) in terms of G (demand for Guatemala Gold) and S (demand for Sumatra Silver). T = a constant times G plus another constant times S. You need to determine
these constants.
c. What is the expected value of the total roasting time needed to handle the total demand for
Guatemala Gold and Sumatra Silver in one month?
d. What is the variance of the total roasting time needed to handle the total demand for
Guatemala Gold and Sumatra Silver in one month?
e. Moonbuck's operations manager has reserved 640 hours on the Clover Machine to process next
month’s demand. Assuming that total roasting time is normally distributed, do you think this will suffice? What is the probability that 640 hours will be enough?

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf given below. f(x, y) = K(x2 + y2) 22 ≤ x ≤ 30, 22 ≤ y ≤ 30 0 otherwise

(a) Compute the covariance between X and Y. (Round your answer to four decimal places.) Cov(X, Y) =

(b) Compute the correlation coefficient p for this X and Y. (Round your answer to four decimal places.) ρ =

Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 11 calls per hour. The arrival rate is 22 calls per hour.

1. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
   
   
   
2. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used? If required, round your answer to four decimal places.
   
   
   
3. What number of calls, in decimal form, receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.
   

Chapter 13

13.1 Jean tests the effects of four different levels of caffeine (no caffeine, 40mg caffeine, 80mg caffeine, 120mg caffeine) on public speaking ability. One group of participants was tested in all four conditions over the course of four weeks – a different condition each week. What statistical analysis should Jean conduct to determine the effect of caffeine on public speaking?

13.2 How does the formula for the repeated-measures ANOVA differ from the formula for the One-way, independent-measures ANOVA?

13.3 Calculate SS_{between subjects} for the following data set. SHOW WORK

Person   Treatment 1       Treatment 2       Treatment 3

A       8           5           7

B       10           4           5

C       6           4           4

D       8           3           6

E       7           6           5

F       8           4           5

13.4 What three hypothesis tests do you have to conduct if you are using a Two-Factor (Factorial) ANOVA to analyze your data? (list/describe each one)

13.5 You can do some basic calculations based on treatment means, to get an idea of what types of effects might be present in a factorial study (even if you can’t say if they are statistically significant). Based on the table of means below, does it look like there could be any main effects or interactions? Specify which ones. SHOW WORK

Use the following scenario and data to answer questions 13.6 - 13.7

Researchers are interested in how serving temperature and pouring method affect the taste of Champagne (more bubbles = better taste). In this 3x2 factorial design, different glasses of Champagne are poured under different conditions; the summary data for the study appear in the table below. The researchers want to know which method is best.

n = 10

N = 60

∑X² = 1150

*Note, low averages mean few bubbles = Champagne is less tasty

13.6 Work through the steps involved in calculating this Factorial ANOVA for the Champagne study. Fill out the ANOVA table below as you go through the steps. Show work for Full Credit and the chance of Partial Credit.

Source               SS           df       MS       F

Between treatments

   Temperature

   Pour

Temperature X Pour

Within treatments

Total

13.7 What critical F value would you use to evaluate the three hypotheses in the Champagne ANOVA?

Temperature critical F =

Pour critical F =

Temperature X Pour critical F =

Chapter 14

14.1 The figure on the right is a scatterplot showing the relationship between drive ratio and horsepower. Based only on the figure, how would you describe this relationship? (Make sure to address its form, direction, and strength.)

Form –

Direction –

Strength –

14.2 What is the biggest limitation a researcher faces when using a correlational design?

14.3 Give one example of a study that would need to use a correlational design?

End of Lab 10!

1. Suppose 50 drug test results are given from people who use drugs (see table below):

If 2 of the 50 subjects are randomly selected without replacement, find the probability that the first person tested positive and the second person tested negative.

_______________

2. A comprehensive final exam in STAT 200 has a mean score of 73 with a standard deviation of 7.8. Assume the distribution of the exam scores is approximately normal. If 24 students are randomly selected, find the probability that the mean of their exam scores is less than 70.

The probability density function of the random variable X is given by fX(x) = ax + 2/9 if 1/2 ≤ x ≤ 3, and 0 otherwise.

(a) Compute the value of a.

(b) Let the random variable Y be defined as Y = [X], where [·] is the “round down” operator (that is, for example, [2.5] = 2, [−2.5] = −3, [−3] = −3). Find the probability mass function of Y . (Hint: For Y to take value k, what values should X take?)

(c) Compute Var(Y )

I am confused with part B.

A researcher has collected the blood samples of 30 individuals and found that the mean hemoglobin concentration for the sample of individuals is 13.9 grams per deciliter and the standard deviation is 1.43 grams per deciliter. Calculate a 99.0% confidence interval for the mean hemoglobin concentration for the population.

[1] (10.22, 17.58)

[2] (13.17, 14.63)

[3] (13.18, 14.62)

[4] (13.23, 14.57)

Course: Marketing Management

For a product of your own choosing, pick one logical variable (e.g., age) that can be used to segment the market. Now add a second variable (e.g., gender) so that customers have to satisfy the categories of both variables simultaneously (e.g., 18 - to 24 year old women).Now add a third variable. How many possiblesignments can you identify from a combination of three variables? What implications does this have for the marketing manager?

Harper's Index reported that the number of (Orange County, California) convicted drunk drivers whose sentence included a tour of the morgue was 542, of which only 1 became a repeat offender.

(a) Suppose that of 1074 newly convicted drunk drivers, all were required to take a tour of the morgue. Let us assume that the probability of a repeat offender is still p = 1/542. Explain why the Poisson approximation to the binomial would be a good choice for r = number of repeat offenders out of 1074 convicted drunk drivers who toured the morgue.

The Poisson approximation is good because n is large, p is small, and np < 10.The Poisson approximation is good because n is large, p is small, and np > 10.     The Poisson approximation is good because n is large, p is large, and np < 10.The Poisson approximation is good because n is small, p is small, and np < 10.

What is λ to the nearest tenth?


(b) What is the probability that r = 0? (Use 4 decimal places.)


(c) What is the probability that r > 1? (Use 4 decimal places.)


(d) What is the probability that r > 2? (Use 4 decimal places.)


(e) What is the probability that r > 3? (Use 4 decimal places.)

Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 48% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.

(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)
P(n) =  

(b) What is the probability that Bob first passes the bar exam on the second try (n = 2)? (Use 3 decimal places.)


(c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.)


(d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.)


(e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass? Hint: Use μ for the geometric distribution and round.

Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials.

(a) Compare P(3 successes), where p = 0.30, with P(2 successes), where p = 0.70.

P(3 successes), where p = 0.30, is smaller.They are the same.     P(3 successes), where p = 0.30, is larger.

(b) Compare P(3 or more successes), where p = 0.30, with P(2 or fewer successes), where p = 0.70.

P(3 or more successes), where p = 0.30, is smaller.They are the same.     P(3 or more successes), where p = 0.30, is larger.

(c) Find the value of P(4 successes), where p = 0.30. (Round your answer to three decimal places.)
P(4 successes) =  

For what value of r is P(r successes) the same using p = 0.70?
r =  

(d) What column is symmetrical with the one headed by p = 0.20?

the column headed by p = 0.85the column headed by p = 0.80     the column headed by p = 0.40the column headed by p = 0.50the column headed by p = 0.70

Smitley and Davis studied the changes in gypsy moth egg mass density over one generation as a function of the initial egg mass density in a control plot and two treated plots. The data below are for the control plot.

A. On the basis of the data given in the table, find the best-fitting logarithmic function using least squares. State the square of the correlation coefficient. (Note that the authors used logarithms to the base 10.) (Use 4 decimal places in your answers.)
y(x) =

r² =

B. Use this model to estimate the change in egg mass density with an initial egg mass of 120 per 0.04 ha. (Use 4 decimal places in your answer.)
With an initial egg mass of 120 per 0.04ha, the change in mass density is

%

Question 1 2 pts

In a sample of 80 adults, 28 said that they would buy a car from a friend. Three adults are selected at random without replacement. Find the probability that none of the three would buy a car from a friend.

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Question 2 2 pts

A sock drawer has 17 folded pairs of socks, with 8 pairs of white, 5 pairs of black and 4 pairs of blue. What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair?

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Question 3 2 pts

An investment advisor believes that there is a 60% chance of making money by investing in a specific stock. If the stock makes money, then there is a 50% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money and receive a dividend.

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Question 4 2 pts

An investment advisor believes that there is a 60% chance of making money by investing in a specific stock. If the stock makes money, then there is a 50% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money and receive a dividend.

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Question 5 2 pts

A smartphone company found in a survey that 6% of people did not own a smartphone, 15% owned a smartphone only, 26% owned a smartphone and only a tablet, 32% owned a smartphone and only a computer, and 21% owned all three. If a person were selected at random, what is the probability that the person would own a smartphone only or a smartphone and computer?