Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.1 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.As the confidence level increases, the margin of error remains the same.     As the confidence level increases, the margin of error increases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval remains the same length.As the confidence level increases, the confidence interval decreases in length.     As the confidence level increases, the confidence interval increases in length.

There are two fast food burger chains near your house. You want to determine which one has the shortest wait times. The last ten times you went to “Dan’s Diner,” the wait times were:

12, 13, 13, 16, 17, 19, 19, 20, 22, 24 (minutes)

You then call the statistician for “Burger Barn” and he tells you the following:
“Our mean wait time is 19 minutes, with a standard deviation of 1.65 minutes. Here is

our 5-number summary: {12, 18, 19, 20, 25}”
a.) (2 pts.) Write a 5-number summary {min, Q1, median, Q3, max} for Dan’s Diner.

b.) (3 pts.) Draw box plots for Dan’s Diner and Burger Barn on the same number line (one above the other).

c.) (3 pts.) Compare the two box plots. Which restaurant has shorter wait times? Use statistical language in your answer.

d.) (3 pts.) Complete the table and calculate the standard deviation for Dan’s Diner. Dan’s Diner: 12, 13, 13, 16, 17, 19, 19, 20, 22, 24

Standard Deviation (round to two decimal places):

e.) (3 pts.) Which burger chain has more consistent wait times? Use statistical language in your answer.

Using Porter’s Five Forces Framework, highlight the factors that would reduce sustainable industry profits (to near zero economic profit).  These factors apply to any industry, but you may find it helpful to think of the airline industry in making your selections.

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.1 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error remains the same.

As the confidence level increases, the margin of error decreases.

As the confidence level increases, the margin of error increases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval increases in length.

As the confidence level increases, the confidence interval remains the same length.    

As the confidence level increases, the confidence interval decreases in length.

1. Life Expectancy Part 3 Refer to the Data Set AllCountries. (Data sets can be found near the bottom of the Read, Study & Practice section of WileyPLUS.) Use the 199 life expectancies listed and StatKey to answer the following questions.

a. Use an equation editor to formulate the null and alternative hypothesis to test the following claim:

“The average life expectancy for all countries is not 68.9 years.”

b. From the AllCountries data, do your best to randomly select 10 of the 213 life expectancies listed. List the 10 values you selected below. (You can use the 10 values from Graded Problem Set 3 if you’d like.)

Bermuda:80.6

Bulgaria: 74.5

Egypt, Arab Rep.: 71.1

Kora Rep: 81.5

Argentina: 76.2

Panama: 77.6

Canada: 81.4

Korea, Dem. Rep.:69.8

Belarus: 72.5

Belize: 73.9

c. Construct a randomization distribution in StatKey to test the above hypothesis. Take at least 1000 samples. Take a screenshot of your StatKey page, and paste it below. (Your graph will differ from other students.)

d. Find and interpret the p-value in regards to the hypothesis and claim.

I have randomly selected the 10 life expectancies from the data set and hopefully, you don't need anything else from the dataset

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.9 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.As the confidence level increases, the margin of error remains the same.     As the confidence level increases, the margin of error increases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.As the confidence level increases, the confidence interval increases in length.     As the confidence level increases, the confidence interval remains the same length.

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

ABC Apartments is a 300-unit complex near Fairway University that attracts mostly university students. The manager has collected the following data and wants to project the number of units leased in Semester 9 using simple linear regression. Here is the information that has been collected:

In answering these questions, you must identify and use the correct independent and dependent variables.

a) The apartment manager wants to forecast the Number of Units Leased as a function of time. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?

b) Suppose the manager believes that the Number of Units Leased is a function only of University Enrollment. It is believed that there will be a one semester lag between the enrollment and the units leased. In other words, the number of units leased in a semester is a function of the university enrollment in the prior semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?

c) Suppose the manager believes that the Number of Units Leased is a function only of the Average Lease Price for that semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9 if the average lease price for that semester is $450?

d) Considering the strength of each of the relationships that you found in parts a) through c), would you use any of these to forecast the Number of Units Leased for Semester 9? Explain your answer.

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

Austin Peay State, a university near Nashville, Tennessee, is applying a data-mining approach to higher education. Before students register for classes, a robot looks at their profiles and transcripts and recommends courses in which they are likely to be successful or have higher chances of success. The software takes an approach similar to the ones Netflix, eHarmony, and Amazon use to make their recommendations. It compares a student’s transcripts with those of past students who had similar grades and SAT scores. When a student logs in, the program offers 10 “Course Suggestions for You.” This recommendation is based on the student’s major and other information related to that student. The goal is to steer students toward courses in which they will make better grades. According to Tristan Denley, a former programmer turned math professor turned provost, students who follow the recommendations do substantially better. In the fall of 2011, 45 percent of the classes that students were taking had been on their top 10 recommendations list. This data-mining concept is catching on. Three other Tennessee colleges now use Denley’s software. Institutions outside the state are developing their own versions of the idea.

1. What are the benefits and drawbacks of this approach to course recommendations?
2. Are there any data that should or should not be included in data mining for this purpose? Why or why not?