The Indiana State Police union is interested in whether the number of miles driven by each trooper is the same or different for the three different 8-hour shifts. Twenty Indiana state troopers were selected randomly selected on each of the three shifts and the number of miles that they traveled was recorded.

a) Is this an observational or an experimental study? Please explain your answer.

b) What is the population in this study?
20 Indiana troopers in each shift.
All police officers
The recorded number of miles
The times of the shift.
The Indiana State Police union
All Indiana State Troopers

c) What is the factor or treatment in this study?
All police officers
20 Indiana troopers in each shift.
All Indiana State Troopers
The times of the shift.
The Indiana State Police union
The recorded number of miles

d) What is the outcome variable of this study?
The Indiana State Police union
All Indiana State Troopers
The recorded number of miles
20 Indiana troopers in each shift.
The times of the shift.
All police officers

e) State a possible source of bias in this study. Feel free to speculate beyond the explicit statement of the question. However, nothing that is assumed can be contradicted by what is stated. Please include any assumptions that you are making.

Problem 4-09 (Algorithmic)

Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon’s management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. Find the optimal solution and determine the total number of call-center employees under the optimal solution. Use a software package LINGO or Excel Solver. If your answer is zero, enter "0".

Let X_i = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday…)

Solution:

Number of excess employees:

Total Number of Employees Under the Optimal Solution=

A new vaccine was tested to see if it could prevent the ear infections that many infants suffer from. Babies about a year old were randomly divided into two groups. One group received​ vaccinations, and the other did not. The following​ year, only 331 of 2454 vaccinated children had ear​ infections, compared to 507 of 2453 unvaccinated children. Complete parts​ a) through​ c) below.

​a) Are the conditions for inference​ satisfied?

A. No. The groups were not independent.

B. No. More than​ 10% of the population was sampled.

C. No. It was not a random sample.

D. Yes. The data were generated by a randomized​ experiment, less than​ 10% of the population was​ sampled, the groups were​ independent, and there were more than 10 successes and failures in each group.

​b) Let Modifying Above p1 be the sample proportion of success in the unvaccinated​ group, and let p2 be the sample proportion of success in the vaccinated group. Find the​ 95% confidence interval for the difference in rates of ear​ infection, p1−p2.

The confidence interval is ( %, %).

​(Do not round until the final answer. Then round to one decimal place as​ needed.)

​c) Use your confidence interval to explain whether you think the vaccine is effective.

A.No. We are​ 95% confident that the rate of infection of vaccinated babies could be as much as 5.1​% higher compared to unvaccinated babies.

B.Yes. We are​ 95% confident that the rate of infection is 5.1 to 9.3​% lower. This is a meaningful​ reduction, considering the​ 20% infection rate among unvaccinated babies.

C. No. No conclusion can be made based on the confidence interval.

D.Yes. We are​ 95% confident that about 9.3​% of unvaccinated babies will get an ear​ infection, while only 5.1% of vaccinated babies will. This is a meaningful reduction.

In the computer game World of Warcraft, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack, and that attacks are independent. During a particular fight, a character has

249

critical strikes out of

588

attacks.

(a) Construct a

99.5%

confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places.

b) Construct a

95%

confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places.

c) What is the effect of increasing the level of confidence on the width of the interval? (narrower, wider)

A Nissan Motor Corporation advertisement read, "The average man's I.Q. is 107. The average brown trout's I.Q. is 4. So why can't man catch brown trout?" Suppose you believe that the brown trout's mean I.Q. is not four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief. (Use a significance level of 0.05.)

An IAB study on the state of original digital video showed that original digital video is becoming increasingly popular. Original digital video is defined as professionally produced video intended only for ad-supported online distribution and viewing. According to IAB data, 30% of American adults 18 or older watch original digital videos each month. Suppose that you take a sample of 1.100 U.S. adults, what is the probability that fewer than 25 in your sample will watch original digital videos?

NEXT QUESTION

Use the following information to answer the next questions:
Sally Soooie believes University of Arkansas students are more generous than students at other SEC schools and believes that this generosity will lead them to sign up to be organ donors more frequently. She takes a random survey of 100 U of A students (Sample 1) and finds that 78 of them have signed the form to be organ donors. A random sample of students from Vanderbilt (Sample 2) found 62 out of 100 are registered organ donors.
  
1.What is the 90% confidence interval for the proportion of Vanderbilt students that are organ donors based on this sample?

2.What would happen to the confidence interval if the professor sampled an additional 100 students to the sample?

Suppose in a local Kindergarten through 12^th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through five. A simple random sample of 600 is surveyed. Calculate the following using the normal approximation to the binomial distribution. (Round your answers to four decimal places.)

(a) Find the probability that less than 250 favor a charter school for grades K through 5.


(b) Find the probability that 315 or more favor a charter school for grades K through 5.


(c) Find the probability that no more than 290 favor a charter school for grades K through 5.


(d) Find the probability that there are fewer than 275 that favor a charter school for grades K through 5.


(e) Find the probability that exactly 300 favor a charter school for grades K through 5.

USE R AND SHOW CODES

2. The following data were collected in a multisite observational study of medical effectiveness in Type II diabetes. These sites were involved: a healthy maintenance organization (HMO), a university teaching hospital (UTH), and an independent practice assumption (IPA). The following data display the treatment regimens of patients measured at baseline by site. Use the data to test that no difference in treatment regimens across sites. (in addition, calculate the expected frequency for each cell.)

                                                                 Treatment regimen

           Site                             Diet            oral Hypoglycemic           Insulin                Total  

           HMO                         294                         827                             579                     1700

           UTH                           132                         288                             352                      772

            IPA                            189                         516                             404                    1109

          Total                           615                       1631                            1335                    3581

Bianca Pascoe has provided the following statement as background and advice in terms of the recommendations you can provide to her organisation.

The number of goods sold by “The Local” is in excess of one million per year with deliveries being about

40% of that figure. The amount of goods sold has decreased marginally in recent years. “The Local” is wholly owned but Bianca and her staff have a standard of living to

maintain so there is some pressure to raise overall sales whilst keeping costs, particularly

delivery costs, in check.   

Bianca continues: It is your job to use the sample data from last year’s overall sales to do

some statistical analyses and interpretations, investigating what the current overall sales of

the business are and providing insights that will guide future business decisions. She

specifically asks: Can you put together a statistical report about the overall sales and

deliveries of “The Local”?

1. Provide a table in which you summarise complete descriptive statistics on ‘Overall sales’

and ‘deliveries’ of the goods represented by your sample data set (including but NOT limited to measures

of central location, measures of variability, etc.). What insights do these statistics provide? Additionally,

please state the coefficient of variation for ‘sales’ and ‘deliveries’ for the entire dataset. Comment on the

results you observe.  

2. Prepare frequency distributions (remember to use Sturge’s rule and create the appropriate

similarly sized classes) and accompanying histograms and ogives for these quantitative sets. Think about and provide additional analyses/diagrams that may be of interest. What insights do these

statistics provide?  

3. Analyse ‘Overall sales’ and ‘deliveries’ for any relationship, providing a scatter plot.  

Comment on the existence of a relationship, how you came to that conclusion, if a

relationship exists further comment on its strength and, in any case, what this means in terms of managing the retail outlet.  

4. Develop cross tabulation or contingency tables to provide information on:  

a. Overall sales and fat/sugar content, please only analyse those goods that have items that

exhibit Regular and Low Fat/Sugar values.  

b. Item Type and deliveries. Remember quantitative values must be presented as classes

in cross tabulation or contingency tables. Be Careful to explain any patterns or anomalies

you find in your tables.  

5. Prepare a pie chart to graphically represent the proportion of overall sales by each item

type (create classes of overall sales for this purpose). Interpret the graph comment on any

issues you perceive.  

World Happiness In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.4 and a standard deviation of 2.2. Find the probability that a randomly selected study participant’s response was (a) less than 4, (b) between 4 and 6, and (c) more than 8. Identify any unusual events in parts (a)–(c). Explain your reasoning.

Please Perform one Chi-square Test by doing the following (Hint: Chapter 15/17, Nonparametric Methods: Chi-Square):

a. Organize the data and show in MS Excel (5 points);

b. Write down one potential question that you could answers using Chi-square test with the Happiness_2011.xls dataset and state its null and alternate hypotheses (5 points);

c. Perform one Nonparametric Methods: Chi-Square Test using any two reasonable variables from the Happiness_2011.xls dataset (two qualitative variables) and show the analysis results for the question (10 points);

d. Indicate whether you reject or accept the null hypothesis (5 points);

e. Interpret your findings from the analysis (5 points).

Please Perform ANOVA One-Factor Analysis by doing the following (Hint: Chapter 12, ANOVA):

a. Organize the data and show in MS Excel (5 points);

b. Write down one question that you could answers using ANOVA One Factor analysis with the Happiness_2011.xls dataset and state its null and alternate hypotheses (5 points);

c. Perform one ANOVA One-Factor analysis using two reasonable variables from the Happiness_2011.xls dataset (one quantitative variable and one qualitative group variable) and show the analysis results for the question (10 points);

d. Indicate whether you reject or accept the null hypothesis (5 points);

e. Interpret your findings from the analysis (5 points).

You are doing some research on the cost of one-bedroom apartments in town. Based on prices from previous years, a real estate agent gives you the information that σ is approximately $55 and μ is approximately $675per month. Assume that price follows roughly a normal distribution. You have randomly selected 25 apartments for which the price was published. The average price for these apartments is ?̅=695. You are to test if μ is less than 675.You set the null and alternative hypotheses as follows:

?0: ?≤ 675 ?? ??: ?>675

a. Compute the test statistic value.

b. If α=0.05, what is the critical value?

c. What is the p value?

d. What is the conclusion if α=0.05?

e. What is the conclusion if α=0.02?

A supermarket chain claims that its customers spend an average of 65.00 per visit to its stores. The manager of a local Long Beach store wants to know if the average amount spent at her location is the same. She takes a sample of 12 customers who shopped in the store over the weekend of March 18-19^th. Here are the dollar amounts that the customers spent:

88

69

141

28

106

45

32

51

78

54

110

83

Calculate the mean and the standard deviation. Run the appropriate test in SPSS. You may choose to evaluate and make a decision based on p-value or critical value from the t-table.

The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions:

A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes?

B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes?

C.            If you randomly select 100 people what is the probability that their average wait time will be at most 24 minutes?

2.            The proportion of people who wait more than an hour at the Social Security Office is 28%. Use this information to answer the following questions:

A.            If you randomly select 45 people what is the probability that at least 34% of them will wait more than an hour?

B.            If you randomly select 60 people what is the probability that between 25% and 30% of them will wait more than an hour?

C.            If you randomly select 150 people what is the probability that less than 23% of them will wait more than an hour?