IDL 3 Preliminary Assignment
For the following problems you will focus on Polya’s first two phases in solving each problem (refer to the Problem Identification Resources Canvas page as needed.). A reminder about populations and samples. “In statistics, a population is an entire group about which some information is required to be ascertained. A statistical population need not consist only of people. We can have populations of heights, weights, BMIs, hemoglobin levels, events, outcomes… In selecting a population for study, the research question or purpose of the study will suggest a suitable definition of the population to be studied,” (Banerjee & Chaudhury, 2010, p. 60).
After reading and evaluating each of the four problems below, answer the questions and submit your answer sheet through the assignment upload. The assignment does NOT require you to determine a statistical method to use or complete the calculations for the problems.
Problem 1
Traffic engineers in Florida want to reduce the rate of accidents between pedestrians and cars at intersections. Research has shown that replacing stoplights with roundabouts (also called traffic circles) can improve safety for bikers and pedestrians. Engineers wanted to test this concept so it can be applied across Florida, and last year, they replaced five timed stoplights in a Florida city with roundabouts. The accident rates at five intersections before the intervention were 5.1, 3.4, 6.1, 4.9, and 4.1 accidents per month. After installing roundabouts, the new rates of pedestrian accidents were 4.5, 3.6, 5.5, 4.8, and 4.1 accidents per month. Does replacing stoplights with roundabouts significantly reduce the rate of accidents at intersections? Use an alpha value of 0.05 in your decision.
Problem 1 Responses
What is known
Look at the data, what is measured? For what unit?
What statistical parameter is important? (What do we want to look at to get an answer?)
·
What unknown (The question that is being answered)? (What is being measured must be the focus of the question)
·
What is the sample? What is the sample size ( n)?
·
What is the bigger thing/group you will know about by using statistical analysis? (the population)
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Problem 2
Ten Pig Farms is a producer of barbecue sauces and pig products. It has recently added a new type of preservative chemical to its barbecue sauce, but customers claim that the sauce is spoiling before the “best if used by” date on the bottle. The chemical engineer hired by Ten Pig Farms claims that the sauce should stay fresh for 100 days after the day it is opened, as long as the bottle is refrigerated. Ten Pig Farm’s quality control engineer ran an experiment on the barbecue sauce to determine whether the new preservative was allowing the sauce to spoil before 100 days. Ten bottles of sauce with the new formula were opened, and every ten days, the quality control intern tried a sample of each sauce and noted whether it tasted fresh. Once the sauce tasted spoiled, the intern made note of day of the last sample. The intern’s determination about how long the sauces stayed fresh is given in the table below. Is the new preservative allowing the sauce to spoil before 100 days, with a 95% confidence level?
| Bottle number | Days of freshness |
| 1 | 100 |
| 2 | 110 |
| 3 | 90 |
| 4 | 110 |
| 5 | 80 |
| 6 | 120 |
| 7 | 110 |
| 8 | 100 |
| 9 | 130 |
| 10 | 100 |
Problem 2 Responses
What is known
·
Look at the data, what is measured? For what unit?
·
What statistical parameter is important? (What do we want to look at to get an answer?)
·
What unknown (The question that is being answered)? (What is being measured must be the focus of the question)
·
What is the sample? What is the sample size ( n)?
·
What is the bigger thing/group you will know about by using statistical analysis? (the population)
·
Problem 3
Blue Fish Media is the owner of an entertainment app where users watch short, minute-long videos. The app uses artificial intelligence to predict new content for its users, based on the app user’s “Liked” and “Disliked” content. The app developer claims that after the app has rated 200 videos, the algorithm will predict favorable content at least 85% of the time. After seeing its daily app users decline, Blue Fish Media decided to test how well the algorithm was working to predict new content. The company ran a test using ten volunteer college students, who were told to download the app and spend some time watching videos at home. The volunteers “liked” any content they enjoyed and “disliked” any videos they didn’t want to finish. The volunteers rated at least 200 one-minute videos so that the algorithm had enough information about the user’s preferences. The volunteers were then brought to a testing room, where they rated videos from the app in front of researchers. They watched twenty videos and chose “like” or “dislike.” The number and percent of liked videos is given below for each volunteer. Is the algorithm successfully predicting favorable content at least 85% of the time? Use an alpha value of 0.05 in your decision.
| Volunteer number | Liked videos ( n/20) | Liked videos (%) |
| 1 | 17 | 85% |
| 2 | 13 | 65% |
| 3 | 15 | 75% |
| 4 | 19 | 95% |
| 5 | 18 | 90% |
| 6 | 11 | 55% |
| 7 | 14 | 70% |
| 8 | 9 | 45% |
| 9 | 15 | 75% |
| 10 | 14 | 70% |
Problem 3 Responses
What is known
·
Look at the data, what is measured? For what unit?
·
What statistical parameter is important? (What do we want to look at to get an answer?)
·
What unknown (The question that is being answered)? (What is being measured must be the focus of the question)
·
What is the sample? What is the sample size ( n)?
·
What is the bigger thing/group you will know about by using statistical analysis? (the population)
·
Problem 4
Answer the following questions about the problem in IDL 3 Final assignment page. This will help you identify the key data points as you form a plan to calculate the answer. Then you will write a paragraph describing your approach to the problem.
Problem 4 Responses
What is known
·
Look at the data, what is measured? For what unit?
·
What statistical parameter is important? (What do we want to look at to get an answer?)
·
What unknown (The question that is being answered)? (What is being measured must be the focus of the question)
·
What is the sample? What is the sample size ( n)?
·
What is the bigger thing/group you will know about by using statistical analysis? (the population)
·
Paragraph Presenting the Data
This must be written as a cohesive paragraph that would be clear, complete, and easy to read by an outside audience. In this paragraph you will provide:
· The context of the problem – Why does this problem exist? Who or what organizations are involved? Where did the problem occur?
· The numerical data and its relevance to the problem you are solving (do not include all the data points, but describe the data using summary statistics)
· Why does having this data allow you to find an answer to the problem? To get to this element of the paragraph, you must think about Polya’s second phase. You do not need to solve the problem yet, only to understand how you can use statistics to get you the answer, given what you know.
Hypothesis Test Questions (to help you write about it)
Do you have sample data or population data?
Do you want to know about the sample or the population to get your answer?
What two critical things will the hypothesis test allow you to evaluate for this problem?
What does the p-value represent?
How do you determine which hypothesis test to use (z or t)?
When you complete the hypothesis test will you have ‘proven’ something?
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