Use SAS. Please include the code and the answers.

1. Generate 625 samples of size 961 random numbers from U(1, 9).

For each of these 625 samples calculate the mean:

a) Find the simulated probability that the mean is between 5 and 5.2.

b) Find the mean of the means.

c) Find the standard deviation of the means.

d) Draw the histogram of the means.

Your Toronto Maple Leafs won 30 of 82 games last season (i.e., the 2014-2015 season), giving them a winning percentage of 37%. If we assume this means the probability of the Leafs winning any given game is 0.37, then we can predict how they would have done in a playoff series.

Answer the following questions to determine the probability that the Leafs would have won a best of 7playoff series (i.e., won 4 games) had they made the playoffs last season.

a. Rephrase this question in terms of sequences of 0s and 1s. What is the shortest length of a sequence? What is the longest length of a sequence?

b. Calculate the number of sequences which correspond to the Leafs winning the series. (Note that the answer is not C(7, 4).)

c. Calculate the number of sequences as they relate to this problem. (Note that the answer is not 27 as not all series would last 7 games.)

d. Calculate the probability that the Leafs would win the series.

e. What is your best guess for the probability that the Leafs will ever win the Stanley Cup again (the ultimate prize in the NHL)

2.

A simple random sample with n = 54 provided a sample mean of 22.5 and a

sample standard deviation of 4.4.

a.

Develop a 90% confidence interval for the population mean.

b.

Develop a 95% confidence interval for the population mean.

c.

Develop a 99% confidence interval for the population mean.

d.

What happens to the margin of error and the confidence interval as the

confidence level is increased?

All answers were generated using 1,000 trials and native Excel functionality.) Suppose that the price of a share of a particular stock listed on the New York Stock Exchange is currently $39. The following probability distribution shows how the price per share is expected to change over a three-month period: Stock Price Change ($) Probability –2 0.05 –2 0.10 0 0.25 +1 0.20 +2 0.20 +3 0.10 +4 0.10 (a) Construct a spreadsheet simulation model that computes the value of the stock price in 3 months, 6 months, 9 months, and 12 months under the assumption that the change in stock price over any three-month period is independent of the change in stock price over any other three-month period. For a current price of $39 per share, what is the average stock price per share 12 months from now? What is the standard deviation of the stock price 12 months from now? Based on the model assumptions, what are the lowest and highest possible prices for this stock in 12 months?

Given a recent outbreak of illness caused by E. coli bacteria, the mayor in a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant’s cleanliness. In order to investigate this possibility, the mayor has five restaurant inspectors grade (scale of 0 to 100) the cleanliness of three restaurants. The results are shown in the accompanying table. (You may find it useful to reference the q table.)

b. If the average grades differ by restaurant, use Tukey’s HSD method at the 5% significance level to determine which averages differ. (If the exact value for n_T − c is not found in the table, use the average of corresponding upper & lower studentized range values. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

A survey of 1320 people who took trips revealed that 108 of them included a visit to a theme park. Based on those survey results, a management consultant claims that less than 9 % of trips include a theme park visit. Test this claim using the ?=0.05

significance level.

Find

(a) The test statistic

(b) The P-value

(c) A or B in conclusion
A. There is not sufficient evidence to support the claim that less than 9 % of trips include a theme park visit.
B. There is sufficient evidence to support the claim that less than 9 % of trips include a theme park visit.

The paired data ((x, y)): (1,6),(5,8),(7,9),(8,0),(4,1) is considered.

(a) Find the pearson correlation coefficient

(b) Find the slope and intercept of the regression coeffients.

(c) What percent of the variation in y is described by variation in x?

Some statistics are not resistant to a single outlier. An example would be the mean value, as one extremely large of small value can tip the scales. Which of these statistics is also not resistant to outliers: median, standard deviation, IQR, range, Pearson correlation, linear regression coefficients?

QUESTION 16

1. Jon reads that 76% of Americans prefer Coke over Pepsi. He works at a local restaurant and decides to poll his customers there about their soda preference. He finds that 120 out of 150 customers surveyed prefer Coke. He would like to conduct a test of hypothesis to see if there is a significant difference between customers at his restaurant and the national results for all Americans, in terms of their preference for Coke over Pepsi. After calculating the test statistic and p-value, what would his statistical conclusion be at an alpha level of 0.10?

   	A.	Yes, do not reject Ho
   	B.	No, do not reject Ho
   	C.	Yes, reject Ho
   	D.	No, reject Ho

QUESTION 19

1. In 2017 it was reported that 46% of Americans still had landline phones in their homes. Researchers would like to see if that percentage has declined since that time. Data was collected in 2019 and of the 655 participating Americans, 265 said they still had landlines in their homes. Is this enough evidence that the percentage of Americans with landlines in their homes has significantly decreased in the past 2 years? Identify the parameter in this problem.

   	A.	true proportion of all Americans in 2019 who use their landline phone as their primary means of contact
   	B.	true proportion of all Americans in 2019 who have a landline phone in their homes
   	C.	true proportion of all Americans who have both a cell phone and a landline phone
   	D.	true proportion of all Americans in 2017 who have a landline phone in their homes

QUESTION 26

1. In 2017 it was reported that 46% of Americans still had landline phones in their homes. Researchers would like to see if that percentage has declined since that time. Data was collected in 2019 and of the 655 participating Americans, 265 said they still had landlines in their homes. Is this enough evidence that the percentage of Americans with landlines in their homes has significantly decreased in the past 2 years? After completing the full hypothesis test, what is the final conclusion?

   	A.	With 95% confidence, I do not have enough evidence to conclude that true proportion of all Americanhouseholds in 2019 that have a landline phone is significantly lower than the 2017 value of 46%.
   	B.	I am 95% confident that the true proportion of all American households in 2019 that have a landline phone is significantly lower than the 2017 value of 46%.

QUESTION 27

1. In 2017 it was reported that 46% of Americans still had landline phones in their homes. Researchers would like to see if that percentage has declined since that time. Data was collected in 2019 and of the 655 participating Americans, 265 said they still had landlines in their homes. Suppose researchers computed a 95% confidence interval for this data. Which of the following would be true?

   	A.	The value of 46% would fall within the interval.
   	B.	The value of 46% would fall outside the interval.

Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 15

Use the​ 68-95-99.7 rule to find the following quantities.

a. The percentage of scores less than

80 is ___%.

​(Round to one decimal place as​ needed.)

b. The percentage of scores greater than 95 is ___​%

​(Round to one decimal place as​ needed.)

c. The percentage of scores between 50 and 95 is ___​%.

​(Round to one decimal place as​ needed.)

In a random sample of four microwave​ ovens, the mean repair cost was $85.00 and the standard deviation was $12.00. Assume the population is normally distributed and use a​ t-distribution to construct a 99​% confidence interval for the population mean mu. What is the margin of error of mu? Interpret the results. The 99​% confidence interval for the population mean mu is?

Wayne is interested in two games, Keno and Bolita. To play Bolita, he buys a ticket for 1 marked with number 1..100, and one ball is drawn randomly from a collection marked with numbers 1,...,100. If his ticket number matches the number on the drawn ball he wins 75, otherwise he hey nothings and loses his 1 bet.

to play keno, he buts a ticket marked with numbers 1..4 and there are only 4 balls marked 1...4; again he wins if the ticket matches the ball draw. if he wins he gets 3, otherwise he loses his bet.

(a) What is the expected payout (expected value of net profit after buying ticket and possibly winning something) for each of these games?

(b) What is the variance and standard deviation for each of these games?

(c) If he decides to play one (and only one) of these games for a very long time, which one should he choose? If he decides to try one of these games for a couple of times, just for fun, which one should he choose?

Problem 6: R simulation.

Use different color lines and appropriate legend to

(1) plot the density functions of χ 2 k for k = 1, 2, 3, 4, 6, 9 in one figure;

(2) plot the density functions of tk for k = 3, 5, 10, 30 and N(0, 1) distribution in one figure. Describe respectively what you observe when the degree of freedom increases.

A random sample of 25 items is drawn from a population whose standard deviation is unknown. The sample mean (x-bar) is 850. Construct a confidence interval with 95% confidence for the different values of s. Do not forget to use the t distribution in this case. a. Assume s = 15. b. Assume s = 30. c. Assume s = 60. d. Describe how the confidence interval changes as s increases.

Nike took a risk on Colin Kaepernick for its “Dream Crazy” #JustDoIt campaign. The first ad aired on national TV September 6, 2018. A year from now they will assess whether the risk paid off. To answer this question they will collect weekly sales data from September 6, 2018 – September 5, 2019 and compare it to 52 weeks of sales data over the previous year, September 6, 2017 to September 5, 2018. For each data point, they will record the date and sales. a. How would you analyze this data? • State the null and alternative hypothesis. • What statistical test would you use?