Stats Sapling Answers

A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to select 120 rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property. The manager gets an SRS of rooms on the first floor with a water view and another SRS of rooms on the 30th floor with a golf course view. What type of sample was obtained?

Stratified random sample

You want to know the opinions of American high school teachers on the issue of establishing a national proficiency test as a prerequisite for graduation from high school. You obtain a list of all high school teachers belonging to the National Education Association (the country's largest teachers' union) and mail a survey to a random sample of 2500 teachers. In all, 1347 of the teachers return the survey. Of those who responded, 32% say that they favor some kind of national proficiency test. Which of the following statements about this situation is true?

The results of this survey may be affected by undercoverage and nonresponse.

𝐵𝑖𝑎𝑠Bias in a sampling method is

any difference between the sample result and the truth about the population that tends to occur in the same direction whenever you use this sampling method.

To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10% of the plots selected using this method:1. Number the plots from 1 to 1410.2. Use a random number generator to select 141 different integers from 1 to 1410.3. Select the corresponding 141 plots. If you used the method described to generate a random sample of 3 plots, which of the following plots could be a legitimate random sample?

115, 540, 876

Your statistics class has 30 students. You want to ask an SRS of 5 students from your class whether they use a mobile device for the online quizzes. You label the students 01, 02, . . . , 30. You enter the table of random digits at this line:14459 26056 31424 80371 65103 62253 22490 61181

14, 03, 10, 22, 06.

You want to take a simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus.You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries

400, 769, 335.

Participation credit for video

:)

To gather information about the validity of a new standardized test for 10th-grade students in a particular state, a random sample of 15 high schools was selected from the state. The new test was administered to every 10th-grade student in the selected high schools.

A cluster sample

Obtaining a simple random sample is either not practical or inappropriate for these hypothetical research studies. Determine which alternative random sampling technique(s) would be appropriate to use for each study. In each case, choose techniques that are efficient and can be used on their own to acquire an unbiased population estimate. More than one technique may be appropriate for a study.

Brianna- Cluster + Multistage Josh- Stratified Emily- Multistage

How much sleep do high school students get on a typical school night? A counselor designed a survey to find out. To make data collection easier, the counselor surveyed the first 100 students to arrive at school on a particular morning. These students reported an average of 7.2 hours of sleep on the previous night. What type of sample did the counselor obtain?

Convenience sample

Researchers randomly selected 1700 people from Canada who had never suffered a heart attack and rated the happiness of each person. Ten years later, the researchers followed up with each person and found that people who were initially rated as happy were less likely to have a heart problem. Which of the following is the most appropriate conclusion based on this study?

Happier people in Canada are less likely to have heart problems

To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10% of the plots. Explain how you would use a random number generator to choose an SRS of 141 plots

Number the plots from 1 to 1410. Use a random number generator to select 141 different integers from 1 to 1410. Select the corresponding 141 plots.

What is the best reason for randomly assigning treatment levels (spraying or not spraying) to the experimental units (farms)?

Random assignment will tend to average out all other uncontrolled factors such as soil fertility so that they are not confounded with the treatment effects.

Two female statistics students asked a random sample of 60 high school boys if they have ever cried during a movie. Thirty of the boys were asked directly and the other 30 were asked anonymously by means of a "secret ballot." When the responses were anonymous, 63% of the boys said "Yes," whereas only 23% of the other group said "Yes." What type of bias is likely present in this study which explains the discrepancy in the two percentages?

Response bias

An SRS of 880 drivers was asked: "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the 880 respondents, 171 admitted that at least one light had been red. What type of bias is present in this study and what is the likely direction of the bias?

Response bias leading to an estimate that is likely too low.

Michigan Stadium, also known as "The Big House," seats over 100,000 fans for a football game. The University of Michigan Athletic Department wants to survey fans about concessions that are sold during games. Tickets are most expensive for seats on the sidelines. The cheapest seats are in the end zones (where one of the authors sat as a student). A map of the stadium is shown. The department select an SRS of fans from each of the three seating zones (sideline, corner, endzone). They then combine these SRSs into one overall sample. What type of sample was obtained?

Stratified random sample

Can texting make you healthier? Researchers randomly assigned 700 Australian adults to either receive usual health care or usual heath care plus automated text messages with positive messages, such as "Walking is cheap. It can be done almost anywhere. All you need is comfortable shoes and clothing." The group that received the text messages showed a statistically significant increase in physical activity. What is the meaning of "statistically significant" in this context?

The difference in physical activity for the two groups is larger than the difference that could be expected to happen by chance alone.

A popular website places opinion poll questions next to many of its news stories. Simply click your response to join the sample. One of the questions was "Do you plan to diet this year?" More than 30,000 people responded, with 68% saying "Yes." Which of the following is true?

The poll uses voluntary response, so the results tell us little about the population of all adults.

Many websites include customer reviews of products, restaurants, hotels, and so on. The manager of a hotel was upset to see that 26% of reviewers on a travel website gave the hotel "1 star"—the lowest possible rating. How could bias in the sampling method affect the estimate?

This is a voluntary response sample. It is likely that those customers that volunteered to leave reviews feel strongly about the hotel, often due to a negative experience. As a result, the 26% from the sample is likely greater than the true percentage of all the hotel's customers who would give the hotel 1 star.

The director of student life at a small college wants to know what percent of students eat regularly in the cafeteria. To find out, the director selects an SRS of 300 students who live in the dorms. What type of bias is present in this study and what is the likely direction of the bias?

Undercoverage bias leading to an estimate that is likely too high.

A study of treatments for angina (pain due to low blood supply to the heart) compared bypass surgery, angioplasty, and use of drugs. The study looked at the medical records of thousands of angina patients whose doctors had chosen one of these treatments. It found that the average survival time of patients given drugs was the highest. What do you conclude?

We can't conclude that drugs prolong life because the groups might differ in ways besides the treatment.

Here is a potential sample survey question. "Some cell phone users have developed brain cancer. Should all cell phones come with a warning label explaining the danger of using cell phones?" Is the question clear? Is it slanted toward a desired response?

clear, slanted

When we take a census, we attempt to collect data from

every individual in the population.

A simple random sample of 1200 adult Americans is selected, and each person is asked the following question: "In light of the huge national deficit, should the government at this time spend additional money to send humans to Mars?" Only 39% of those responding answered "Yes."

probably understates the percent of people who favor sending humans to Mars.

A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to select 120 rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property. The manager surveys the registered guest in every room on each of 3 randomly selected floors. What type of sample was obtained?

Cluster random sample

Michigan Stadium, also known as "The Big House," seats over 100,000 fans for a football game. The University of Michigan Athletic Department wants to survey fans about concessions that are sold during games. Tickets are most expensive for seats on the sidelines. The cheapest seats are in the end zones (where one of the authors sat as a student). A map of the stadium is shown. The department selects several numbered sections and survey all of the fans in those sections. What type of sample was obtained?

Cluster random sample

Suppose that 35% of the voters in a state are registered as Republicans, 40% as Democrats, and 25% as Independents. A newspaper wants to select a sample of 1000 registered voters to predict the outcome of the next election.

No, because not all possible groups of 1000 registered voters had the same chance of being chosen.

A corporation employs 2000 male and 500 female engineers. A stratified random sample of 200 male and 50 female engineers gives every individual in the population the same chance to be chosen for the sample. Is it an SRS?

No, every possible sample of 250 engineers does not have the same chance of being selected.

A total of 300 people participated in a free 12-week weight-loss course at a community health clinic. After one year, administrators emailed each of the 300 participants to see how much weight they had lost since the end of the course. Only 56 participants responded to the survey. The mean weight loss for this sample was 13.6 pounds.

Nonresponse bias leading to an estimate that is likely too high.

You want to ask a sample of high school students the question "How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?" You try out this and other questions on a pilot group of 5 students chosen from your class. You use a line of Table D to choose an SRS of 5 students from the following list. Which line of the following sampling procedure contains a mistake?

Step 1

The sales force for a publishing company is constantly on the road trying to sell books. As a result, each salesperson accumulates many travel-related expenses that he or she charges to a company-issued credit card. To prevent fraud, management hires an outside company to audit a sample of these expenses. For each salesperson, the auditor prints out the credit card statements for the entire year, randomly chooses one of the first 20 expenses to examine, and then examines every 20th expense from that point on. Which type of sampling method is the auditor using for each salesperson?

Systematic random sampling

A local news agency conducted a survey about unemployment by randomly dialing phone numbers until it gathered responses from 1000 adults in its state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey.

The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.

How much sleep do high school students get on a typical school night? A counselor designed a survey to find out. To make data collection easier, the counselor surveyed the first 100 students to arrive at school on a particular morning. These students reported an average of 7.2 hours of sleep on the previous night. Is 7.2 hours probably greater than or less than the true average amount of sleep last night for all students at the school and why?

The estimate of 7.2 hours is probably less than the true average because students who arrive first to school had to wake up earlier and may have gotten less sleep than those students who are able to sleep in.

A high school's student newspaper plans to survey local businesses about the importance of students as customers. From an alphabetical list of all local businesses, the newspaper staff chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the staff. Identify the population and the sample. Identify the population and the sample.

The population is all local businesses. The sample is the 73 businesses that return the questionnaire.

A large retailer prepares its customers' monthly credit card bills using an automatic machine that folds the bills, stuffs them into envelopes, and seals the envelopes for mailing. Are the envelopes completely sealed? Inspectors choose 40 envelopes at random from the 1000 stuffed during a given hour for visual inspection.

The population is the 1000 envelopes stuffed during a given hour. The sample is the 40 randomly selected envelopes.

You wonder if TV ads are more effective when they are longer or repeated more often or both. So you design an experiment. You prepare 30-second and 60-second ads for a camera. Your subjects all watch the same TV program, but you assign them at random to four groups. One group sees the 30-second ad once during the program; another sees it three times; the third group sees the 60-second ad once; and the last group sees the 60-second ad three times. You ask all subjects how likely they are to buy the camera. Which of the following best describes the design of this experiment?

This is a completely randomized design with two explanatory variables (factors).

The owner of a large restaurant is considering a new "no tipping" policy and wants to survey a sample of employees. The policy would add 20% to the cost of food and beverages and the additional revenue would be distributed equally among servers and kitchen staff. The owner would like to select a stratified random sample of approximately 30 employees. What should the owner use as strata? type of employee (servers, kitchen staff) Explain your choice of strata. Stratified random sampling might be preferred in this context because the opinion of the employees (servers, kitchen staff) might be the same within each type, but differ across the different type of employee (servers, kitchen staff) . Why might stratified random sampling be preferred in this context?

Using strata will help provide a more precise estimate of the overall proportion who approve of the no tipping policy. Describe how to select a stratified random sample of approximately 30 employees. Select an SRS of 15 employees that are servers and 15 employees that work in the kitchen . Finally, combine these two SRSs into one overall sample .

Tonya wanted to estimate the average amount of time that students at her school spend on Facebook each day. She gets an alphabetical roster of students in the school from the registrar's office and numbers the students from 1 to 1137. Then Tonya uses a random number generator to pick 30 distinct labels from 1 to 1137. She surveys those 30 students about their Facebook use. Tonya's sample is a simple random sample because

it gave every possible sample of size 30 an equal chance to be selected.