List the characteristics of a multinomial experiment. (Select all that apply.)

The number of successes is evenly distributed over all k categories.

We are interested in x, the number of events that occur in a period of time or space.

The trials are independent.

The experiment consists of n identical trials.

Its mean is 0 and its standard deviation is 1.

The outcome of each trial falls into one of k categories.

The experiment contains M successes and N − M failures.

The probability that the outcome of a single trial falls into a particular category remains constant from trial to trial.

The probability that the outcome of a single trial falls between two categories is equal to the area under the curve between those categories.

We are interested in x, the number of successes observed during the n trials.

The experimenter counts the observed number of outcomes in each category.

Each trial results in one of only two possible outcomes.

A diagnostic test has a 95% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probability of giving a (false) positive result when given to a person who doesn’t have the disease. It is estimated that 15% of the population suffers from this disease.

(a) What is the probability that a test result is positive?

(b) A person recieves a positive test result. What is the probability that this person actually has the disease? (probability of a true positive)

(c) A person recieves a positive test result. What is the probability that this person doesn’t actually have the disease? (probability of a false negative)

Two cards are drawn one after the other from a standard deck of 52 cards.

(a) In how many ways can one draw first a spade and then a heart?
(b) In how many ways can one draw first a spade and then a heart or a diamond?
(c) In how many ways can one draw first a spade and then another spade?

(d) Do the previous answers change if the first card is put back in the deck before the second card is drawn?

Note that the book states to use a value of 25% if you don’t know what a good value is for the population estimate. Would we want to use this value in planning election polling? Why or why not? What would be the sample sizes needed to get a 95% confidence interval of plus or minus 3% given that the initial estimate of the population proportion is either 1%, 25%, 50%, 75% or 99% (calculate the five intervals). What do you notice that is interesting?

A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below.

1. Find the correlation coefficient: r=r=   Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ?ρμr == 0
   H1:H1: ?rρμ ≠≠ 0
   The p-value is: (Round to four decimal places)
   
3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
   • There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds.
   • There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds.
   • There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not appropriate.
   • There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the regression line is useful.
4. r2r2 = (Round to two decimal places)
5. The equation of the linear regression line is:   
   ˆyy^ = + xx   (Please show your answers to two decimal places)
   
6. Use the model to predict the percent of seeds that sprout if the plant produces 57 seeds.
   Percent sprouting = (Please round your answer to the nearest whole number.)

Please answer the following:

1. United Dairies, Inc., supplies milk to several independent grocers throughout Dade County, Florida. Managers at United Dairies want to develop a forecast of the number of half gallons of milk sold per week. Sales data for the past 12 weeks are:

1. Compute four-week and five-week moving averages for the time series.

1. 1. Compute the MSE for the four-week and five-week moving average forecasts.
   2. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? The MSE for three weeks is 23527.78
2. Show the exponential smoothing forecasts using α = 0.1.
   1. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α=0.1 or α= 0.2 for the United Dairies sales time series?
   2. Are the results the same if you apply MAE as the measure of accuracy?
   3. What are the results if MAPE is used?

3.    Use exponential smoothing with a α = 0.4 to develop a forecast of demand for week 13. What is the resulting MSE?

8. SAC Community Clinic is interested in knowing how far their patients commute (from their homes). To date, 20,000 unique patients have received care at the facility; the clinic operates Monday through Friday and sees about 20 patients per day. You have been commissioned to conduct a survey of their patients to gather home addresses, mode of transportation, and round trip commute time. Your goal is to gather data on 10% of the patients who enter the clinic for a week. You will use a simple random sampling. a. Define the population b. Define the sample frame c. Explain how you would select the sample d. Explain how you would gather the data.

A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 8 out of 12 questions correctly. What is the chance of this, if ;

a. You go into the exam without knowing a thing, and have to resort to Pure guessing?

b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.

c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing.

In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a "normative" group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are in the table below.

What is the maximum possible amount that could be awarded under the "2-standard deviations rule"? (Round all intermediate calculations and the answer to three decimal places.)

Three decision makers have assessed utilities for the following decision problem (payoff in dollars): State of Nature Decision Alternative S1 S2 S3 d1 10 60 -20 d2 90 100 -80 The indifference probabilities are as follows: Indifference Probability (p) Payoff Decision maker A Decision maker B Decision maker C 100 1.00 1.00 1.00 90 0.95 0.80 0.85 60 0.85 0.70 0.75 10 0.75 0.55 0.60 -20 0.60 0.25 0.50 -80 0.00 0.00 0.00 Find a recommended decision for each of the three decision makers, if P(s1) = 0.30, P(s2) = 0.55, and P(s3) = 0.15. (Note: For the same decision problem, different utilities can lead to different decisions.) If required, round your answers to two decimal places. Decision maker A EU(d1) = _______ EU(d2) = _______ Recommended decision: _______ Decision maker B EU(d1) = _______ EU(d2) = _______ Recommended decision: _______ Decision maker C EU(d1) = _______ EU(d2) = _______ Recommended decision: _______

2. Dee Pressants owns Dee’s Pharmacy located in a small medical office building. Dee estimates that 20% of her prescription business comes from referrals from Dr. Mel Practice. For the next 25 prescription customers, what is the probability that a. 6 or less were referred by Mel? b. Between 3 and 6 were referred by Mel? c. At least 4 were referred by Mel? d. Exactly 5 were referred by Mel? e. Dee makes $10 profit per prescription but has to pay Mel a $3 kickback on any referrals. What is the expected profit from the 25 customers?

I have the answers for these questions, according to my study guide. I don't understand how the answers were obtained, though, so please show work!

A) You are planning to take two exams. According to the records, the failure rates for the two exams are 15% and 25%, respectively. Additionally, 80% of the student who passed the exam 1 passed exam 2. (The 80% is based on the given condition.)

What will be the probability that you fail the 1st exam, if you did not pass the 2nd exam?

0.32

B) You are planning to take two exams. According to the records, the failure rates for the two exams are 15% and 25%, respectively. Additionally, 80% of the student who passed the exam 1 passed exam 2. (The 80% is based on the given condition.)

What is the probability that you will fail at most one exam?

0.92

C) You are planning to take two exams. According to the records, the failure rates for the two exams are 15% and 25%, respectively. Additionally, 80% of the student who passed the exam 1 passed exam 2. (The 80% is based on the given condition.)

Given that you have passed at least one of the exams, what is the probability that you have passed only one exam?

0.2609

1. Igor Beaver is a salesman for Planet of the Grapes, a medium sized winery near Solvang. Igor is going on a sales trip visiting 10 restaurants throughout Southern California. Historically, Igor convinces 30% of the restaurants he visits to stock and sell his wine. a. What is the expected number of restaurants that Igor will close a sale on this trip? b. Find the variance. What is the probability that on this sales trip Igor make sales at c. 4 restaurants or less? d. Between 2 and 4 restaurants? e. Exactly 4 restaurants? f. At least 5 restaurants? g. Igor gives each new client a gift. How many gifts should he take on the trip to be at least 99% sure that he has enough? h. Find and plot the probability distribution and cumulative distribution using Excel.

A business owner believed that a higher percentage of females than males bought items from her stores. To test her belief, she conducted a study. What might her research hypothesis be?

A. p = .5

B. p > .5

C. p > .5 (greater than or equal to symbol)

D. not enough information

Given:

What are the confidence limits (alpha = 0.05) for the true mean value of Y when X = 3?