Historical data indicated that the time required to service the conveyor belt at Coca-Cola Amatil's Richlands operations can be modelled as a normal distribution with a standard deviation of 20 minutes. A random sample of 20 services revealed a mean service duration of 119.9 minutes. Determine a 90% confidence interval for the mean service time in minutes. State the lower bound of this interval correct to two decimal places.

The question in the textbook says:

"One study mentioned in an article that 90% of the students scored above the national average on standardized tests. Using your knowledge on mean, median and mode, explain why the school reports are incorrect. Does your analysis change if the term "average" refers to mean? To median? Explain what effect this misinformation might have on the perception of the nation's schools."

I really do not know how to answer this question, please help.

1. A toxicologist was interested in the effects of an insecticide on the mortality of a certain type of beetle. Six groups of beetles were exposed to various concentrations (C) of the insecticide. At the end of the experiment dead beetles in each group were counted.

concentration	10.8	11.6	12.1	12.6	13.1	13.5
death	15	24	26	24	29	29
group size	50	49	50	50	50	49

Consider the logistic regression model

logit [P(death at concentration C)] = β0 + β1 ×C

1. Write down the contribution to the likelihood function from the first group (that is, the group with death=15, size=50 and C = 10.8).
2. Re-write the above for the log-likelihood function.
3. Write down the contribution to the likelihood function from the last group (that is, the group with death=29, size=49 and C = 13.5).
4. Re-write the above for the log-likelihood function.
5. Use proc fcmp to write a SAS program that computes the log-likelihood function for the above application. In other words, your function accepts two numbers as values of β0 and β1, and outputs the log-likelihood function evaluated at the prescribed input values. Use the testing values β0 = 2 and β1 = 3 to make sure that you function works properly (it should give you a value of −5795.3).
6. Use SAS proc logistic to find the ML estimates and the corresponding maximized log-likelihood function value. Use your own function developed in part (5) to verify the SAS results.
7. By adding or subtracting 10% from the ML estimates, you can create four pairs of (β0,β1). Compute the log-likelihood function for all these 4 pairs of parameter values. Can you find a larger log-likelihood function value than that evaluated at the ML estimates? Why?

2) Revisit the toxicology example: six groups of beetles were exposed to various concentrations

(C) of the insecticide. At the end of the experiment dead beetles in each group were counted.

concentration	10.8	11.6	12.1	12.6	13.1	13.5
death	15	24	26	24	29	29
group size	50	49	50	50	50	49

Consider the logistic regression model

logit[P(death at concentration C)] = β0 + β1 X C

1. Under the assumption β1 = 0, write down the log-likelihood function (of _0 alone).
2. Write a SAS program to draw the above log-likelihood function.
3. Use SAS to find the ML estimate β0 under the assumption β1 = 0.
4. Use your own SAS program to find the maximized log-likelihood function value at the above ML estimate of _0. Compare your results with what SAS reports.
5. Using results from Homework 2, calculate the likelihood ratio test statistics for testing H0 : β1 = 0 vs. HA : β1 ≠0.
6. What is the p-value of the above?
7. Calculate the OR comparing two concentrations, one of which is 0:4 units higher than the other.
8. Calculate the estimated probability of beetle death at concentration C = 12:4.
9. Use SAS to draw a graph relating probability of beetle death to concentration.

A pawn shop is open to purchasing goods that may not have been acquired through honest means. Every time the shop makes a questionable transaction there is a probability that the sale gets busted by the local police. The owner estimates that the probability that any single transaction will be busted is 2% independent from all others. He also estimates that the net profit he makes on one transaction is well-described by a normal distribution with average $50 with standard deviation of $15.

i. How much profit can they expect to see before the operation is busted?

ii. Find the standard deviation for total profit.

iii. A local police chief, for a monthly fee of $100, can make sure that they are not bothered as often, effectively reducing probability of a bust on each transaction to 0.5%. Suppose that they do 1 questionable transaction a day. Estimate whether they can expect to make more or less profit if they pay the bribe?

A repairman has 20 jobs that need to be completed today. Usually, 70% of all jobs are fairly straightforward, so that the time it takes to complete them is well-described by normal distribution with average 10 minutes and standard deviation 1 minute. The rest are challenging jobs, so that completion time is well-modeled with exponential distribution with average 1 hour.

i. If she starts at 8am, what is the expected time when she will finish all already assigned jobs?

ii. When asked when she will finish the jobs, she wants to give a safe answer by overestimating it by one standard deviation. Find the standard deviation for the time needed to finish all jobs.

A study examined parental influence on the decisions of teenagers from a certain large region to smoke. A randomly selected group of​ students, from the​ region, who had never smoked were questioned about their​ parents' attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found​ that, among the

263

students who indicated that their parents disapproved of kids​ smoking,

53

had become established smokers. Among the

43

students who initially said their parents were lenient about​ smoking,

18

became smokers. Do these data provide strong evidence that parental attitude influences​ teenagers' decisions about​ smoking? Complete parts a through i below.

​a) What kind of design did the researchers​ use?

A prospective observational study

Your answer is correct.

An experimental study

A retrospective observational study

​b) Write the appropriate hypotheses. Let

p1

be the proportion of students whose parents disapproved of smoking who became smokers. Let

p2

be the proportion of students whose parents were lenient about smoking who became smokers.

Choose the correct answer below.

A.

H0​:

p1minus

p2equals

0

HA​:

p1minus

p2greater than

0

B.

H0​:

p1minus

p2equals

0

HA​:

p1minus

p2not equals

0

Your answer is correct.

C.

H0​:

p1minus

p2not equals

0

HA​:

p1minus

p2equals

0

D.

H0​:

p1minus

p2greater than

0

HA​:

p1minus

p2equals

0

​c) Are the assumptions and conditions necessary for inference​ satisfied?

A.

​No, because the Independent Groups Assumption is not satisfied.

B.

​Yes, all of the assumptions and conditions are satisfied.

Your answer is correct.

C.

​No, because the​ Success/Failure Condition is not satisfied.

D.

​No, because the​ 10% Condition is not satisfied.

E.

​No, because the Randomization Condition is not satisfied.

​d) Test the hypothesis and state the conclusion.

Determine the test statistic.

zequals

negative 3.13

​(Round to two decimal places as​ needed.)

Find the​ P-value.

Pequals

. 002

​(Round to three decimal places as​ needed.)

State the conclusion. Use a significance level of

alpha

equals0.10

.

Choose the correct answer below.

A.

Do not reject

the null hypothesis. There

is

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

B.

Do not reject

the null hypothesis. There

is not

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

C.

Reject

the null hypothesis. There

is not

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

D.

Reject

the null hypothesis. There

is

sufficient evidence that parental attitude influences​ teenagers' decisions about smoking.

Your answer is correct.

​e) Explain in this context what your​ P-value, P, means. Choose the correct answer below.

A.

If the observed difference is the true​ difference, then there is about a

​(100 times

​P)%

chance that there is no difference in the proportions.

B.

If there is no difference in the​ proportions, there is about a

​(100 times

​P)%

chance of seeing the observed difference or larger by natural sampling variation.Your answer is correct.

C.

There is about a

​(100 times

​P)%

chance that there is no difference in the proportions.

D.

There is about a

​(100 times

​P)%

chance that there is a difference in the proportions.

​f) If that conclusion is actually​ wrong, which type of error was​ committed?

A.

A Type

II

error was committed because the null hypothesis is

false

​,

but was

not

rejected.

B.

A Type

Upper I

error was committed because the null hypothesis is

true

​,

but was

mistakenly

rejected.

Your answer is correct.

​g) Create a 90​%CI for the difference of two​ proportions,p 1 minus p 2

. I am having trouble with G.)

[Counting and Probability] Consider the experiment of flipping a coin four times.

a. Using a tree, determine the probability of one or two tails, with a biased coin with P(H) = 2/3. Compare to the probability with an unbiased coin

b. [Bayes’ Rule] Using the results of the part a suppose we have two coins, one unbiased, and a biased coin with P(H) = 2/3. We select a coin at random, flip it three times, and observe either one or two tails. What is the probability we started with the biased coin?
[Hint: use a two-level tree, with the second level using the probabilities from a.]

Define and discuss the difference between linear regression and multiple regression. Are there any assumptions which must be met before using multiple regression?

Scenario

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?

Please provide a new answer old ones where incorrect.

• Suppose reaction time for drag racers is know to be on average 50 ms with a standard deviation of 10 ms and that reaction time is normally distributed.

1. • What is the reaction time that separates the fastest 10% of racers from the rest?
2. What is the interval that contains the middle 95% of racers?
3. Above what value would you expect to find the slowest 60%?

Can you please explain in detail? plus i know for this problem we have to use this formula X= z x standard deviation + mean. Where do i get the z for this problem? i know the mean and Standard deviation but where am i supposed to get the Z?

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 30 0 20 12 19 18 23 −22 −24 −21 y: 11 −5 9 8 21 25 22 −3 −7 −2 (a) Compute Σx, Σx2, Σy, Σy2. Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.) x y x s2 s (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) x y Lower Limit Upper Limit Use the intervals to compare the two funds. 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 25% of the returns for the stock fund fall within a wider range than those of the balanced fund. (d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.) x y CV % % Use the coefficients of variation to compare the two funds. For each unit of return, the stock fund has lower risk. For each unit of return, the balanced fund has lower risk. For each unit of return, the funds have equal risk. If s represents risks and x represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain. A smaller CV is better because it indicates a higher risk per unit of expected return. A smaller CV is better because it indicates a lower risk per unit of expected return.

Suppose there is a normally distributed population which has a mean of μ = 440and a standard deviation of σ = 60. (15p)

1.What portion of a normal distribution is below 295?

2. What z-score would correspond to a raw score of 260?

3. What raw score would correspond to a z score of -3.5?

4. If we randomly select one score from this population, what is the probability that will be less than 550?

5. If we randomly select one score from this population, what is the probability that will be greater than 580?

"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L).

1.9

2

5.7

4.4

1.9

8.7

3.9

6.8

(a) Find the mean, median, and mode. (Round your answers to two decimal places.)

mean
median
mode

(b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.)

s
CV	%
range

(c) Based on the data, would you recommend radon mitigation in this house? Explain.

Yes, since the median value is over "acceptable" ranges, although the mean value is not.Yes, since the average and median values are both over "acceptable" ranges.    No, since the average and median values are both under "acceptable" ranges.Yes, since the average value is over "acceptable" ranges, although the median value is not.

Respond to all of the following questions in your posting for this week:

• Describe the characteristics of the F distribution. Provide examples.
• What are we testing when we test for two population variances? Explain your answer and provide an example.
• What are the assumptions of an ANOVA, and when would you use an ANOVA?

Suppose certain coins have weights that are normally distributed with a mean of

5.641 g5.641 g

and a standard deviation of

0.069 g0.069 g.

A vending machine is configured to accept those coins with weights between

5.5215.521

g and

5.7615.761

g.

a. If

300300

different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?The expected number of rejected coins is

2525.

​(Round to the nearest​ integer.)b. If

300300

different coins are inserted into the vending​ machine, what is the probability that the mean falls between the limits of

5.5215.521

g and

5.7615.761

​g?The probability is approximately

(missing data)

​(Round to four decimal places as​ needed.)