South Shore Construction builds permanent docks and seawalls along the southern shore of long island, new york. Although the firm has been in business for only five years, revenue has increased from $320,000 in the first year of operation to $1,116,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars:

a. Use Excel Solver to find the coefficients of a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. Round your answers to two decimal places.

F_t = _ + _Qtr1 + _Qtr2 + _Qtr3

b. Let Period = 1 to refer to the observation in Quarter 1 of year 1; Period = 2 to refer to the observation in Quarter 2 of year 1; . . . and Period = 20 to refer to the observation in Quarter 4 of year 5. Using the dummy variables defined in part (b) and Period, develop an equation to account for seasonal effects and any linear trend in the time series using Excel Solver. Round your answers to two decimal places. If your answer is negative value enter minus sign.

F_t = _ + _Qtr1 + _Qtr2 + _Qtr3 + _Period

Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales for year 6. Round your answers to one decimal place.

Quarter 1 forecast =

Quarter 2 forecast =

Quarter 3 forecast =

Quarter 4 forecast =

All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has two screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 4 passengers per minute. On Monday morning the arrival rate is 4.8 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 3 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning.

1. The facility manager's goal is to limit the average number of passengers waiting in line to 8 or fewer. How many screening stations must be open in order to satisfy the manager's goal?
   
   Having 2  station(s) open satisfies the manager's goal to limit the average number of passengers in the waiting line to at most 8.
   
2. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places.
   
   W =  minutes

QUESTION FIVE

1. The diameter of shafts produced in a machine follows a normal distribution with the variance of 81mm. A random sample of 36 shafts taken from the production has its mean diameter of 30mm. Find a 95% confidence interval for the diameter of shafts.

2. The Marketing manager of a company feels that 42% of retailers will have enhanced weekly sales after introducing an advertisement at the point of sales. A sample of 36 retailers shops of the company, where the point of sales advertisement has been displayed, reveals that only 18 of them are having enhanced sales after displaying the advertisement. Find the 95% confidence interval for the proportion representing the enhanced sales.

c. The Finance manager of a company feels that 55% of branches will have enhanced yearly collection of deposits after introducing a hike in interest rate. Determine the sample size such that the mean proportion is with plus or minus 0.05 confidence level of 90%?     

An auto insurance company concludes that 30% of policyholders with only collision coverage will have a claim next year, 40% of policyholders with only comprehensive coverage will have a claim next year and 50% of policyholders with both collision and comprehensive coverage will have a claim next year. Records show 60% of policyholders have collision coverage 70% have comprehensive coverage and all policyholders have at least one of these coverages.

Calculate the percentage of policyholders expected to have an accident next year.

1. 10%

2. 20%

3. 31%

4. 36%

5. 40%

**Must be a clear and logical response in 150 to 200 words to the following questions/prompts, providing specific examples to support your answers. Type answers.**

• Which of the statistical techniques have the most usefulness for a business of interest or the job that you are currently in? What is the technique and why is it useful to the business or job?

(St Petersburg Paradox). Suppose you have the opportunity to play the following game. You flip a fair coin, and if it comes up heads on the first flip, then you win $1. If not, then you flip again. If it comes up heads on the second flip, then you win $2, and if not you flip again. On the third flip, a heads pays $4, on the fourth $8, and so on. That is, each time you get tails, you flip again and your prize doubles, and you get paid the first time you flip heads.

a) How much should you be willing to pay to play this amazing game? In other words, compute the expected payout from playing this game.

b) Now suppose the casino (or wherever you’re playing this game) has a limited bankroll of $2^n. So, if you get tails n times in a row, then the game is over automatically and you are paid $2^n. Now what is the expected payout? How much should you be willing to pay to play the game if n = 10?

1. The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. For a single randomly selected movie, find the probability that this movie's production cost is between 51 and 56 million dollars.
4. For the group of 46 movies, find the probability that the average production cost is between 51 and 56 million dollars.

2. Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.1 month. 18 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )  
2. What is the distribution of x¯? x¯ ~ N( , )
3. What is the probability that one randomly selected person learned to walk when the person was between 10 and 12.5 months old?
4. For the 18 people, find the probability that the average age that they learned to walk is between 10 and 12.5 months old.
5. For part d), is the assumption that the distribution is normal necessary? Yes or No
6. Find the IQR for the average first time walking age for groups of 18 people.
   Q1 = ______ months
   Q3 = ______ months
   IQR: ______ months

3. The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 8 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 78.2 and 84.2.
4. For the 8 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 78.2 and 84.2.

4. The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is 7.2 mm. Suppose that 17 individuals are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 17, find the probability that the average hand length is more than 187.
3. Find the third quartile for the average adult male hand length for this sample size.

5. Suppose that the average number of Facebook friends users have is normally distributed with a mean of 125 and a standard deviation of about 55. Assume fourteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 14, find the probability that the average number of friends is less than 107.
3. Find the first quartile for the average number of Facebook friends

6. The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 9 mL. Suppose that 41 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 59.2 mL.
4. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 57.7 mL and 59.2 mL

***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

7) For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.

a. What is the probability that the debt for a borrower with good credit is more than $18,000?

b. What is the probability that the debt for a borrower with good credit is less than $10,000?

c. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?

d. What is the probability that the debt for a borrower with good credit is no more than $14,000?

***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

6) The time needed to complete a final examination in a particular college course is normally distributed with a mean of 90 minutes and a standard deviation of 15 minutes. Answer the following questions.

a. What is the probability of completing the exam in one hour or less?

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 105 minutes?

c. Assume that the class has 60 students and that the examination period is 120 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

Given that z is a standard normal random variable, find z for each situation.

a. The area to the left of z is .9750.

b. The area between 0 and z is .4750.

c. The area to the left of z is .7291.

d. The area to the right of z is .1314.

e. The area to the left of z is .6700.

f. The area to the right of z is .3300.

A company manager believes that a person’s ability to be a leader is directly correlated to their zodiac sign. He never selects someone to chair a committee without first evaluating their zodiac sign. An irate employee sets out to prove her manager wrong. She claims that if zodiac sign truly makes a difference in leadership, then a random sample of 200 CEO’s in our country would reveal a difference in zodiac sign distribution. She finds the following zodiac signs for her random sample of 200 CEO’s:

Can she conclude that zodiac sign makes a difference in whether or not a person makes a good leader?

Hypotheses:

H₀: There is a difference/no difference in leadership ability based on zodiac sign.

H₁: There is a difference/no difference in leadership ability based on zodiac sign.

Enter the test statistic - round to 4 decimal places.

___

Enter the p-value - round to 4 decimal places.

___

Can it be concluded that there is a statistically significant difference in leadership ability based on zodiac sign?

Yes/No

A Gallup Poll showed that 44% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 25 Americans are selected.

Find the probability that no less than 7 Americans are satisfied with the way things are going.

Find the probability that exactly 15 Americans are not satisfied with the way things are going.

Find the probability that the number of Americans who are satisfied with the way things are going differs by greater than 2 from the mean.

Find the probability that greater than 7 Americans are satisfied with the way things are going.

Find the probability that at least 15 Americans are not satisfied with the way things are going.

Find the probability that no more than 9 Americans are satisfied with the way things are going.

Find the probability that more than 40% but at most 65% of these Americans are satisfied with the way things are going.

Round to 4 decimals.

An elementary school started a special reading enrichment program for seventh-graders that has been underway for eight months. One of the investigators wants to confirm the program is having its intended effect, and collects a sample of 34 students from the program with a standardized reading test average of 24.1. The standardized reading test average for seventh-graders in the country is 26.1 with a standard deviation of 4.9. What can the investigator conclude with α = 0.01?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- the school seventh-graders in the program the program months seventh-graders in the country
Sample:
---Select--- the school seventh-graders in the program the program months seventh-graders in the country

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

The standardized reading test of seventh-graders in the special reading enrichment program is significantly higher than seventh-graders in the country.The standardized reading test of seventh-graders in the special reading enrichment program is significantly lower than seventh-graders in the country.    The standardized reading test of seventh-graders in the special reading enrichment program is not significantly different than seventh-graders in the country.

A company that makes language learning software wants to determine which of two approaches (Method A or Method B) to learning vocabulary would lead to the largest number of recalled words. The company wishes to evaluate the methods on 7 different languages (since languages differ in difficulty). Seven individuals, one per language, were recruited to learn words using Method A, and 7 individuals, one per language, were recruited to learn words using Method B.

After one month, each person completed a test of word recall. The data, representing the number of words recalled, are shown in the table below.

The company wishes to test whether there is a difference in the average number of words recalled between the two methods. Calculate the test statistic for this hypothesis to two decimal places. Take all calculations toward the final answer to three (3) decimal places