A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample​ (in years). Assume that the data come from a distribution that is Normally distributed.

Neighborhood 1: 50, 68, 65, 52, 53, 54

Neighborhood 2: 33, 32, 44, 38, 54, 51

​a) Find a 95​% confidence interval for the mean​ difference μ1- μ2​, in ages of houses in the two neighborhoods. (Round to two decimal places as needed)

​b) Is 0 within the confidence​ interval?

(Yes or No)

​c) What does the confidence interval suggest about the null hypothesis that the mean difference is​ 0?

A.Reject H0 since 0 is a plausible value for the true mean difference.

B. Fail to reject H0 since 0 is a plausible value for the true mean difference.

C.Reject H0 since 0 is not a plausible value for the true mean difference.

D.Fail to reject H0 since 0 is not a plausible value for the true mean difference.

Let X ~ Geometric (p) where 0 < p <1

a) Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold.

R 0 - different parameter values have different functions.

R 1 - parameter space does not contain its own endpoints.

R 2. - the set of points x where f (x, p) is not zero and should not depend on p.

R 3. One derivative can be found with respect to p.

R 4. Two derivatives can be found with respect to p.

b) Find the maximum likelihood estimator of p, call it Yn for this problem.

c) Is Yn unbiased? Explain.

d) Show that Yn is consistent asymptotically normal and identify the asymptotic normal variance.

e) Variance-stabilize your result in (d) or show there is no need to do so.

f) Compute I (p) where I is Fisher’s Information.

g) Compute the efficiency of Yn for p (or show that you should not!).

according to a 2009 Reader's Digest article, people throw away approximately 16% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 209 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.1 and 0.16?

Correct answer is 0.4909, can u show me how.

(1)Using the Matlab code developed in Software Assignment #1:

a. Convert the code that generates the random number (H,T) with equal probabilities into a function called myBernolli(p, S) that takes as an input the probability of success p and S is the outcome defined as success (either T or H) and returns the outcome of the trial (either T or H).

b. Test that your function is actually producing the successful outcome with probability p by running the function in a loop of 1000 trials and counting how many times success is produced (it should be close to p*1000).

c. Write a Matlab function called myBinomial(n,p) that takes as an input the total number of trials n, the probability of success p and the outcome defined as success S and uses myBernolli() to return as an output the number of successes x.

d. Write a Matlab function called myGeometric() that takes as an input the probability of success p and the outcome defined as success S and uses myBernolli() to return as an output the number of trials till first success x.

e. Verify that myBinomial() and myGeometric() generates values that follow Binomial and Geometric Distributions by running each of them 5000 times in a loop and plotting a histogram of the random variable x generated from each.

Hints: Random numbers with probability p are generated in Matlab using the command function rand(). Read the help on Matlab to know how to use the function by typing help rand in Matlab command line. Histogram plots [hist()] is a function in Matlab. Read its help to know how to produce

H0: u >= 20

Ha: u< 20

A sample of 50 provided a sample mean of 19.6. The population standard deviation is 1.4.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 3 decimals)?

c. Using = .05, can it be concluded that the population mean is less than 20, Yes or no

d. Using = .05, what is the critical value for the test statistic?

e. State the rejection rule: Reject H0 if z is (select, >=, >, <=, <, =, or not = ) the critical value

f. Using = .05, can it be concluded that the population mean is less than 20? Yes or No

This dataset includes the number of work hours for each project, the function point count for each project, and identifiers for operating system, data management system, and programming language utilized.

Open the dataset pointworkload.csv in Excel. Create a new column that calculates the number of work hours per function point for each project.

Import the file you revised in Excel to include work hours per function point into SPSS

Interpret the slope by circling the correct answers and filling in the blanks. See pp. 194-195 in the course text.

“If the distance between the fire and nearest fire station [ increases | decreases ] by ___________ mile(s), the amount of damage [ increases | decreases ] by ___________ thousand dollars, on average.”

Look online and find an article published within the past 4 weeks that includes a reference to probabilities, means, or standard deviations.  These articles might be discussing weather events, investing outcomes, or sports performance, among many other possible topics.

Write the equation (formula) for a residual and then calculate its value “by hand” for the observation in the data set whose distance between the fire and nearest fire station (in miles) is 3.0; show your work. Based on this value, was the observation overestimated (below average) or underestimated (above average) by the regression? Explain. See page 191 in the course text.

Does the y-intercept for this regression model have practical meaning in this context? If so, interpret it. Otherwise, explain why not. Recall, the value of the explanatory variable is 0 for the y-intercept. See page 195 in the course text.

Generate the Simple linear regression results and Parameter estimates table in StatCrunch for the least-squares regression equation and include them with your submission.

You are at a wetland site. You have been instructed to test for chromium contamination. Suppose that a regulatory agency has determined that a population mean chromium concentration equal to 7 mg/kg characterizes the no-contamination state. Likewise, a population mean chromium concentration significantly greater than 7 mg/kg characterizes the contamination state. Suppose that 12 soil tests were conducted around different areas around the wetland site. Their chromium concentration analyzed with the following results. Use this information for the first 9 problems. Do not round show all steps for problem.

6.223 6.995 10.333 7.265 7.833 7.111

6.986 8.934 9.167 7.505 7.301 7.213

1. Describe the population of interest and hypothesized parameter for this scenario.

2. Find the mean of the sample. Use the formula and show the steps for finding the sample mean.

3. Find the median of the sample. Use the formula and show the steps for finding the sample median.

4. Find the standard deviation of the sample. Use the formula and show the steps (add steps to another page if necessary).

5. Using the appropriate symbols, write the hypotheses.

6. Calculate the test statistic showing the work with the formula.

7. Using StatCrunch, determine the p-value for the hypothesis test using the appropriate probability distribution (do not just use the t test for a single mean output).

8. Make the decision for the test in terms of the null hypothesis. Explain how you arrive at this decision.

9. Write the conclusion with minimal statistical jargon and answer the research question of interest as demonstrated in the presentations.

Use the given information to find the number of degrees of​ freedom, the critical values chi Subscript Upper L Superscript 2 and chi Subscript Upper R Superscript 2​, and the confidence interval estimate of sigma. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 80​% ​confidence; n=27​, s=0.29 mg.

Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem.

Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer’s office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, after the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer’s office and an average of 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. The downtime cost (wait time and service time) for customers is $100 per hour.

OEI is planning to expand its business. Within 1 year, OEI projects that it will have 20 customers, and within 2 years, OEI projects that it will have 30 customers. Although OEI is satisfied that one service technician can handle the 10 existing customers, management is concerned about the ability of one technician to meet the average 3-hour service call guarantee when the OEI customer base expands. In a recent planning meeting, the marketing manager made a proposal to add a second service technician when OEI reaches 20 customers and to add a third service technician when OEI reaches 30 customers. Before making a final decision, management would like an analysis of OEI service capabilities. OEI is particularly interested in meeting the average 3-hour waiting time guarantee at the lowest possible total cost.

Managerial Report

Develop a managerial report (1,000-1,250 words) summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 and then 30 customers, and justify your response. Include a discussion of the following issues in your report:

1. What is the arrival rate for each customer?
2. What is the service rate in terms of the number of customers per hour? (Remember that the average travel time of 1 hour is counted as service time because the time that the service technician is busy handling a service call includes the travel time in addition to the time required to complete the repair.)
3. Waiting line models generally assume that the arriving customers are in the same location as the service facility. Consider how OEI is different in this regard, given that a service technician travels an average of 1 hour to reach each customer. How should the travel time and the waiting time predicted by the waiting line model be combined to determine the total customer waiting time? Explain.
4. OEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information: (a) probability that no customers are in the system, (b) average number of customers in the waiting line, (c) average number of customers in the system, (d) average time a customer waits until the service technician arrives, (e) average time a customer waits until the machine is back in operation, (f) probability that a customer will have to wait more than one hour for the service technician to arrive, and (g) the total cost per hour for the service operation.
5. Do you agree with OEI management that one technician can meet the average 3-hour service call guarantee? Why or why not?
6. What is your recommendation for the number of service technicians to hire when OEI expands to 20 customers? Use the information that you developed in Question 4 (above) to justify your answer.
7. What is your recommendation for the number of service technicians to hire when OEI expands to 30 customers? Use the information that you developed in Question 4 (above) to justify your answer.
8. What are the annual savings of your recommendation in Question 6 (above) compared to the planning committee's proposal that 30 customers will require three service technicians? (Assume 250 days of operation per year.) How was this determination reached?

Both Alice and Bob toss a fair coin three times. The probability that Alice records a different numbers of heads than Bob is given by A/B, where A and B are relatively prime integers (greatest common divisor is 1). Find A + B.