Laura has decided to offer a meeting at her house as her birthday. For this, it has prepared several quantities of 3 types of cocktails: tom collins, cubalibre, mojito
The dynamics that Laura uses for her guests to choose the drinks is to pack the cocktails in dark glasses so that their selection is completely random. Furthermore, it has been established that the selection must be independent of the previous one.
The probability of choosing each of the cocktails is given by a survey that Laura made to 30 of her friends, the answers to which are presented below:
1. 4 people showed liking for the 3 types
2. 8 people like both tom collins and cubalibre
3. 11 like both tom collins and mojito
4. 2 people like only the mojito
5. 4 people like only the tom collins
6. 3 people like only the cubalibre

Assume that each of the surveyed friends showed a taste for one or more cocktails.

If the first 3 cocktails were selected there was one of the tom collins, find the probability that the eighth cocktail selected is the fourth of the cocktail tom collins?

1. Online customer service is a key element to successful online retailing. According to a marketing survey, 6.8% of online customers take advantage of the online customer service. Random samples of 210 customers are selected. What is the standard error of all possible sample proportions?

2. A researcher wants to create a 90% confidence interval for the population proportion, with the margin of error of 4%. She has no idea what the population proportion is and she cannot take a trial sample. Calculate the required sample size.

5. Confidence Intervals Suppose you have the following X: (6, 5, 4, 1, 1). What is the mean of X? What is the Standard deviation of X? What is the Standard Error of X? Calculate the 95% confidence interval for X. Calculate the 99% confidence interval for X.

The probabilities of an individual having a particular blood type are listed below.

            Type A                        .4

            Type B                        .3

            Type AB                     .25

            Type O                        .05

9.   Find the probability that a randomly selected individual will have type A or type b blood.

10. Find the probability that a randomly selected individual will have a blood type other than type AB.

11. Find the probability that a randomly selected individual will have type AB or type O.

12. Find the probability that a randomly selected individual has a blood type other than type A or type B.

The appraisal of a warehouse can appear straightforward compared to other appraisal assignments. A warehouse appraisal involves comparing a building that is primarily an open shell to other such buildings. However, there are still a number of warehouse attributes that are plausibly related to appraised value. Consider the accompanying data on truss height (ft), which determines how high stored goods can be stacked, and sale price ($) per square foot.

(a)

Estimate the true average change in sale price associated with a one-foot increase in truss height, and do so in a way that conveys information about the precision of estimation. (Use a 95% CI. Round your answers to three decimal places.)

$  , $

(b)

Estimate the true average sale price for all warehouses having a truss height of 25 ft, and do so in a way that conveys information about the precision of estimation. (Use a 95% CI. Round your answers to three decimal places.)

  ,

dollars per square foot

(c)

Predict the sale price for a single warehouse whose truss height is 25 ft, and do so in a way that conveys information about the precision of prediction. (Use a 95% PI. Round your answers to three decimal places.)

  ,

dollars per square foot

How does this prediction compare to the estimate of (b)?

The prediction interval is  ---Select--- the same as smaller than wider than the confidence interval in part (b).

(d)

Without calculating any intervals, how would the width of a 95% prediction interval for sale price when truss height is 25 ft compare to the width of a 95% interval when height is 30 ft? Explain your reasoning.

Since 25 is  ---Select--- farther from nearer to the mean than 30, a PI at 30 would be  ---Select--- wider smaller than the PI at 25.

(e)

Calculate the sample correlation coefficient. (Round your answer to three decimal places.)

Interpret the sample correlation coefficient.

There is a  ---Select--- weak strong correlation between the variables.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

A roulette wheel has 38 slots: 18 red, 18 black, and 2 green. A ball is tossed into the wheel and eventually settles in a slot at random. You play many games, betting $1 on red each time. If the ball lands in a red slot you win $1, otherwise you lose the dollar you bet. After n games, what is the probability that you have more money than you started with? Give (approximate) numerical answers for n = 100 and n = 1000. How would the answer change if there were no green slots?

GPA of the students who are taking Stat 50 class at bcc follows a normal distribution with a mean of 2.87 and a standard deviation of 0.43. If 35 students who are taking Stat 50 are selected, what is the probability that their average GPA is more than 2.97?

A) Not enough information is given to find the answer

B) Almost 0

C) 0.084

D) 0.408

2) GPA of the students who are taking Stat 50 class at bcc follows a normal distribution with a mean of 2.87 and a standard deviation of 0.43. If one student who is taking Stat 50 are selected, what is the probability that his or her average GPA is more than 2.97?

A) Not enough information is given to find the answer

B) 0.408

C) Almost 0

D) 0.084

Scientist looked at 7 patients with edemas. They researched the fovea thickness in 7 eyes pre and post surgery. The results presented from surgery are

shown in the following table:

Subject: Pre-op Thickness: Post-op Thickness: Difference (Pre minus Post)

1 200 690 -490

2 840 280 560

3 470 230 240

4 690 200 490

5 560 730 -170

6 500 210 290

7 440 200 240

A) Find out whether we should conclude that surgery is effective on reducing foveal thickness. Compute the observed value of the test statistic for the Sign test and calculate a p-value within the tables accuracy. To calculate p-value use poisson table.

B) Using the Wilcoxon signed rank test compute the observed test statistic

C) Talk about the validity of utilizing either the Wilcoxon signed-rank test, the sign test, and the paired t-test for these data. What assumptions must be made for each of these test to be valid?

MUST SHOW / EXPLAIN ALL WORK BY HAND

Use the following table to find the T statistic for inference on the difference of two means of 0.99 and 1 carats

0.99 Carat( pt= 99, X= 44.50, S= 13.32

1 Carat (pt= 100, X= 53.43, S= 12.22

Use the above table to find the degree of freedom(df)

Discuss the Utility of concomitant variable in design of experiment. Thank you

Find a data set on the internet. Some suggested search terms: Free Data Sets, Medical Data Sets, Education Data Sets.

1. Introduce your Data Set and Cite the Source.
2. What trends do you notice in your data set?
3. Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two tailed) would you have to complete?
4. Explain the steps needed to complete the Hypothesis Test. What is needed?

Given: trying to determine if grading practices are consistent with the rest of their department. Historical data indicated the department's overall grade distribution for the course this instructor teaches is the following:

A/A-: 54% B+/B/B-: 28% C+/C/C-: 11% D+/D/D-: 3% F: 2% other: 2%

following the semester final grades are shown below for the course:

A/A-: 53 B+/B/B-" 36 C+/C/C-: 12 D+/D/D-: 5 F:1 other: 3 total: 110 to test this consistency, the instructor will use a chi-square goodness-of-fit test

Q7: construct the null and alternative hypotheses for this test

Q8:Determine the expected counts assuming the null is trie for the following categories. A/A-, B+/B/B-, C+/C/C-, D=/D/D-, F, other

Q9: perform the chi-square goodness-of-fit test at the .05 significance level

1. What are the three main ways of assigning a probability?

2. List four possible outcomes needed to determine probabilities?

3. An experiment consists of three stages. There are three possible outcomes in the first stage, four possible outcomes in the second stage, and two possible outcomes in the third stage. What is the total number of outcomes?

4. A box has 12 balls. If 3 balls are randomly selected with replacement from the box, how many possible samples are there?

5. 3 students will be selected from a tutorial class of 25 students for lucky prize. First student will get $50, second student $30 and third gets $10, how many possible outcomes are there?

6. A box has 20 balls. If 5 balls are randomly selected without replacement from the box, how many possible samples are there?

7. What are 4 types of probabilities?

8. The probability that price of a Economics text book (A) will increase over next semester is 0.5 while probability that the price of an Accounting text book (B) will rise over the same period is 0.7. The probability that price of both text books will rise is 0.4.

Follow the 3 steps to get the answers of the following questions:

a) What is the probability that the price of the Economics text book will not rise over the next semester?

b) What is the probability that neither book price will rise?

c) Given that the price of the Accounting text book does not rise, what is the probability that the price of the Economics text book will rise?

d) Give your opinion and justify the answer that whether price rises for two text books are mutually exclusive or not?

9. Differentiate between Discrete Random Variable and Continuous Random Variable?

10. Classify the following in either Discrete Random Variable or Continuous Random Variable and state the reason for your answer:

1. X = the number of students attending lab on Monday

2. X = the number of teachers in Oxford

3. X = the weight of a new born baby

4. X = the average number of students passed their Mid term test in a random sample of 10 tutorial classes

11. What is the probability distribution of a random variable when the coin is tossed twice describing the number of heads that turn up? Show all the steps.

12. What are the four conditions for Binomial Experiment?

13. According to the records, 30% of the businesses in US does sponsor in large scale. Just this morning 10 businesses sponsored.

1. What is the expected number of businesses that sponsor?

2. What is the standard deviation of the number of businesses that sponsor?

STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established:

Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held.

Optimal Solution:

Macy’s purchases model 505 straight-leg, blank ink denim jeans for women from Levis Straus & Co and sells them to consumers in 185 store locations across 35 U.S. states. Levis Straus & Co’s cost-of-goods-sold for each pair of these model 505 straight-leg, blank ink denim jeans for women is $21.85. Levis Straus & Co sells these model 505 jeans to Macy’s for $34.50 each. Macy’s in-turn sells each pair of these jeans to consumers for a suggested retail price of $58.49.

What is Macy’s mark-up, is $US dollars and %, on each pair of model 505 straight-leg, blank ink denim jeans for women from Levis Straus & Co sold at the suggested retail price? Assume Macy’s includes model 505 straight-leg, blank ink denim jeans for women from Levis Straus & Co in the end-of-year sale (November 1st to December 31st) when every item in the store is discounted by 17.5% off the suggested retail price.

What is the discounted price Macy’s customers will pay for model 505 straight-leg, blank ink denim jeans for women from Levis Straus & Co? What is Macy's revised Mark-Up % after applying the 17.5% discount? Assume Macy’s sells-through a quantity of 21,333 model 505 straight-leg, blank ink denim jeans for women at the discounted price during the end-of-year sale.

What is the total revenue and, separately, gross margin in $US dollars, for Levis Straus & Co?

What is the total revenue and, separately, mark-up in $US dollars, for Macy’s?