In each of the following situations, state which of the following items in the STAT-TESTS menu would be the most appropriate.

BOB’S SERVICE STATION AND DINER “Sylvia, we have been operating this service station and diner for many years. Lately, I have the feeling that my income has declined. I think that there are opportunities out there that I have not taken advantage of. I want to pass this business on to my sons and am not comfortable with our current position and strategy.” The words above, spoken to Sylvia, the primary accountant for Bob’s, reveal a number of concerns Bob has concerning his operation. Bob’s Service Station and Diner (Bob’s) is an independently owned service station and restaurant on a major interstate highway. Bob has been in operation for over a decade and customers have liked to frequent his business. Often they choose their routes to stop at places like his with low fuel prices and to enjoy food like the juicy burgers and good food Bob’s provides. He has a great reputation with his customers, especially truckers, and enjoys their business. Bob has noticed, however, that when busiest with truckers, fewer families stop by. Bob has made a pretty good living running the place. However, even though his income continues to seem satisfactory, it does not seem to buy as much as before. This perception, as well as the maturity of his sons, Jason and Bob Jr., has heightened Bob’s concern over the future of his operation. Bob wants to know what he can do to make this a more profitable business and pass on a more effective operation to his sons. Bob knows that his operation attracts many commercial truckers. However, he is also popular with families stopping to use the facilities and eat in the restaurant after filling up the family vehicle on vacations. Over the past decade Bob’s typical markup on diesel is about 1 cent and on gasoline is about 1.5 cents. This fuel pricing follows the typical process in this business of taking the delivery price and marking it up between 1 and 5 cents per gallon. Bob has also noticed an ebb and flow by season – summer and winter being highest and spring and fall being lower. (Winter is December, January, February. Summer is June, July and August.) Bob knows that he has some control over fuel prices and can alter the prices of his typical meal. The dilemma he faces is to know in what direction he should change them or whether or not he should modify his pricing practice at all. Also, he does not know what other activities or attractions he could add that might increase his profits. If he raises prices, he knows that he will reduce sales. At lower prices, he will sell more but incur greater costs. Bob is getting ready to step back from his business and turn the operation over to his sons. Before he does that, he wants to be comfortable in leaving his sons with a well-defined pricing strategy, based upon data. Following up on the expression of Bob’s future concerns, Sylvia, his accountant, has gathered a substantial amount of information regarding his firm’s performance over the past decade. This data is available in an Excel file on the course web site. Specifically, Bob wants to know: 1. Whether or not recent inflation eroded his income? 2. Whether he should continue with his current fuel pricing practice of marking up diesel by 1 cent and gasoline by 1.5 cents per gallon? Should this practice continue even if fuel prices rise over $4.00 per gallon? 3. How seasonal demand affects his sales and what might be done to take better advantage of these fluctuations?

QUESTION: Use simple regression to estimate the marginal profit contribution from fuel sales. Use it again to estimate the marginal profit contribution from food sales. Compare and interpret your estimates.

Please find DATA here:

https://docs.google.com/document/d/1QVLqoKTu5iSq62HBgmAh1nx0WtYi3bgDBNDkr1pqW5I/edit?usp=sharing

The number of cell phones per 100 residents in countries in Europe is given in table #9.3.9 for the year 2010.  The number of cell phones per 100 residents in countries of the Americas is given in table #9.3.10 also for the year 2010 ("Population reference bureau," 2013).  Find the 98% confidence interval for the different in mean number of cell phones per 100 residents in Europe and the Americas.

Table #9.3.9: Number of Cell Phones per 100 Residents in Europe

Table #9.3.10: Number of Cell Phones per 100 Residents in the Americas

1. ) State the random variable and the parameter in words.

b.) If needed, state the null and alternative hypotheses and the level of significance and don't "bump" them into one line (refer to the textbook)

Ho :

HA :

a =

c.) State and check the assumptions for a hypothesis test

d.) Find the sample statistic, test statistic, and p-value, confidence interval

e.) Conclusion

Since the p-value……..fail to reject or reject   H o or confidence intervals...

f.) Interpretation ( statistical and real world)

What type are each of these: discrete, continuous, or categorical?

and What level are each: interval, ordinal, ratio, nomial?

-Number of Contacts on your phone
-The high daily temperature in San Jose
-The name of a college a student attends

1.6) Mention the business implications of performing ANOVA for this particular case study.

Question 2

Suppose the waiting time of a bus follows a uniform distribution on [0, 20]. (a) Find the probability that a passenger has to wait for at least 12 minutes. (b) Find the mean and interquantile range of the waiting time.

Question 3
Each year, a large warehouse uses thousands of fluorescent light bulbs that are burning 24 hours per day until they burn out and are replaced. The lifetime of the bulbs, X, is a normally distributed random variable with mean 620 hours and standard deviation 20 hours.

1. (a) If a light bulb is randomly selected, how likely its lifetime is less than 582 hours?

2. (b) The warehouse manager orders a shipment of 500 light bulbs each month. How

   many of the 500 bulbs are expected to have a lifetime that is less than 582 hours?

3. (c) The supplier of the light bulbs and the manager agree that any bulb whose lifetime

   is among the lowest 1% of all possible lifetimes will be replaced at no charge. What is the maximum lifetime a bulb can have and still be among the lowest 1% of all lifetimes?

Question 4
60% of students go to HKUST by bus. There are 10 students in the classroom. (a) What is the probability that exactly 5 of the students in the classroom go to

HKUST by bus?
(b) What is the mean number of students going to HKUST by bus?

Question 5
Peter is tossing an unfair coin that the probability of getting Head is 0.75. Let X be the random variable of number of trails that Peter get the first Head.
(a) Find the probability that the number of trails is five.
(b) Find the mean and standard deviation of random variable, X.

Question 6

Given that the population proportion is 0.6, a sample of size 1200 is drawn from the population.

1. (a) Find the mean and variance of the sampling distribution of sample proportion.

2. (b) Find the probability that the sample proportion is less than 0.58.

3. (c) If the probability that the sample proportion is greater than k is 0.6, find the value of k.

Question 1

The random variables X & Y are independent. E[X] = 5, E[Y] = 7, Var[X] = 4,

Var[Y] = 6. Calculate following expectation and variance. ( ?[?] =

? ,???[?]=?2) ??

(a) E[5X+6]
(b) E[6Y+3]
(c) E[X-Y+11]
(d) Var[3X+10000] (e) Var[-4Y-1234567] (f) Var[2X-3Y]

A player pays $ 13 to roll three six-sided balanced dice. If the sum of the 3 dice is less than 13, then the player will receive a prize of $ 70. Otherwise, you lose the $13.
a. Find the expected value of profit.

USE THE FOLLOWING DIRECTION FOR 1A AND 1B: In 2010, a random sample of 250 dog owners was taken and it was found that 140 owned more than one dog. Recently, a random sample of 400 dog owners showed that 200 owned more than one dog. Do these data indicate that the proportion of dog owners owning more than one dog has decreased? Use a 5% level of significance, and p1= proportion of dog owners who owned more than one dog in 2010. If you conduct hypothesis testing, you have to consider:

a. one-tailed test

b. two-tailed test

c. one-tailed test because sample proportions are different.

d. two-tailed test because sample size is large.

1b.) Assuming computed Z of 1.04 for the test, what is your conclusion?

a. Reject H0. Proportion of dog owners owning more than one dog has decreased.

b. Fail to reject H0. Proportion of dog owners owning more than one dog has decreased.

c. Reject H0. Proportion of dog owners owning more than one dog has not decreased.

d. Fail to reject H0. Proportion of dog owners owning more than one dog has not decreased.

e. None of the above.

1c.) A Rutgers University professor claims that there is no significant difference between proportion of female (f) and male students (m) of the university who exercise at least 15 minutes a day. What would be a proper conclusion if he collects data, conducts hypothesis test, and finds P-value of 0%.

a. Reject H0. There is a significant difference. --> I THINK THIS IS THE ANSWER BUT I JUST WANT TO KNOW WHY

b. Reject H0. There is no significant difference.

c. Fail to reject H0. There is a significant difference.

d. Fail to reject H0. There is no significant difference.

1d.) A Rutgers University professor claims that female students study more than male students. What would be a proper conclusion if he collects data from random sample of 200 males and sample of 343 females, and finds P-value of 0.65?

a. Reject H0. Female students study more than male students.

b. Fail to reject H0. Female students study more than male students.

c. Fail to reject H0. Female students study less than male students.

d. Fail to reject H0. Female students study almost the same as male students. ---> I THINK THIS IS THE ANSWER I JUST WANT TO KNOW WHY

(25) Consider a population {1,2,3} which has only three numbers. (5) What are the relationships of the individuals of a random sample, namely X_1,X_2…,X_n (5) If we sample with replacement from this population with sample size =2, what is the distribution of sample mean (Distribution table)? (5) If we sample without replacement from this population with sample size=2, what is the distribution of the sample mean (Distribution table)? (10) If we sample with replacement from this population with sample size=100, state the theorem for finding the distribution of the sample mean. What is the distribution of the sample mean (including the mean and variance)?

Hello, i have this excersice in R studio

Write a function in R that generates simulations of a Poisson random variable as follows: define I = [λ], and use p_i + 1 = λp_i / (i + 1) to determine F recursively. Generate a random number U, determine if X≤I by comparing if U≤F (I). If X≤I searches downwards starting at I, otherwise it searches upwards starting from I + 1. Compare the time it takes for the two algorithms in 5000 simulations of a Poisson random variable with parameter λ = 10,200,500.

example

# Poisson usando Inversión
rpoisI <- function(lambda = 1){
  U <- runif(1)
  i <- 0
  p <- exp(-lambda)
  P <- p
  while(U >= P){
    p <- lambda * p / (i + 1)
    P <- P + p
    i <- i + 1
  }
  i
}
sims_pois <- rerun(2000, rpoisI()) %>% flatten_dbl()

ggplot() +
    geom_histogram(aes(x = sims_pois, y = ..density..), binwidth = 1)

As part of a project for their Intro Stat course, two students compared two brands of chips, Frito Lays and Golden Flakes, to see which company gives you more for your money. Five bags of each brand (which, according to the label, each contained 35.4 grams) were measured with a very accurate scale. Use the Wilcoxon Rank-Sum test to see if there are any significant differences between the two brands in the amount of product they put in their bags.
Frito Lays: 35.3 35.4 35.8 35.9 35.9
Golden Flake: 35.3 37.8 38.8 38.1 42.5 8.
1. The null hypothesis is about:
(a) the mean contents of the bags for Frito Lays and Golden Flakes brands
(b) the mode of the contents of the bags for Frito Lays and Golden Flakes brands
(c) the distribution of the contents of the bags for the two brands
(d) the number of bags with contents below the label weight for the two brands 9.

2. The alternative hypothesis, according to the problem stated above, is that:
(a) Frito Lays gives you more chips than Golden Flakes
(b) Frito Lays gives you less chips than Golden Flakes
(c) Frito Lays gives you either more or less chips than Golden Flakes
(d) Golden Flakes gives you more chips than the amount stated on the label 10.

3. The bags that contained 35.9 grams will receive a rank of:
(a) 4
(b) 4.5
(c) 5
(d) 5.5

4. The p-value for the test was 0.1164. We conclude that:
(a) Frito Lays gives you more chips.
(b) Golden Flakes gives you more chips.
(c) There is not enough evidence to prove a difference between the two brands.
(d) There is enough evidence to prove a difference between the two brands

5. If the assumptions for the Normal based procedure were satisfied, we could analyze the data with a confidence interval for:
12
(a) μ
(b) μ1-μ2
(c) μd
d) η1- η 2

6. Why is it not a good idea to use the Normal-based procedure here?
(a) the data was not randomly selected
(b) the data does not have a continuous distribution
(c) the outlier violates the assumption of Normality
(d) the nonparametric method is always better

7. Which of the following kinds of data should be analyzed with non-parametric procedures?
(a) normal
(b) continuous
(c) ranks
(d) all of the above

8. Given that all the necessary assumptions for each test are satisfied, which are more powerful at finding significant differences?
(a) Nonparametric procedures, since their assumptions are generally easier to satisfy.
(b) Normal-based procedures, since they take into consideration the shape of the distribution.
(c) Nonparametric procedures, since their assumptions are generally harder to satisfy.
(d) Normal-based procedures, since they work for distributions of almost any shape.

10.2) John has two unfair coins, and he claims that they are from the same model with the probability of obtaining a head being 0.4. Coin A is tossed 100 times and 38 heads are observed. Coin B is tossed 200 times and 86 heads are observed. At the significance level α being 0.05, check whether these two coins are identical

1. John is going to take a quiz with 10 MC questions. Each question has only one correct answer out of 4 choices. Suppose John simply answer each question by random guess,
   1. (5) What is the probability of have 5 questions answered correctly?
   2. (5) What is the expected number and standard deviation of the questions answered correctly?
   3. (10) If a correct answer counts for 1 point and a wrong answer causes 1 point deduction,
      1. list out all the possible points of this quiz.
      2. what is the expected points of John’s quiz?

1. A (maybe unfair) coin is tossed 100 times and 40 heads are obtained. At significance level α= 10%, do you think that the coin is fair? Use large-sample test for hypothesis testing.