topics 3.1 - 3.4 Sampling methods and problems in sample survey

To randomly select 25 basketball players from the 300 players in the NBA, I would:

• Number the players from 01-25, read 3 digits at a time from a random table, discarding repeats and numbers over 25, and then stop when I reach 25.

• Number the players from 01-299, read 2 digits at a time from a random table, discarding repeats and numbers over 300, and stop when I reach 25.

• Number the players from 0-299, read 2 digits at a time from a random table, discarding repeats and numbers over 299, and stop when I reach 25.

• Number the players from 001-300, read 3 digits at a time from a random table, discarding repeats, 000 and numbers over 300, and stop when I reach 25.

Tags

CCSS.7.SP.A.2

Regina is investigating the opinions of students at her high school on the new school hours proposed by the school board. Which of the following is her population of interest?

• All members of the school board

• All teachers at her school

• All students at her high school

• All students in the school district

Answer explanation

C. Kristen is investigating the opinions of the students at her high school, so her population of interest is all the students at her high school.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

A sample of students will be selected from all the students at a high school. Which of the following sampling methods is least likely to produce a representative sample of the students?

• From a list of all student names, randomly select 50 names from the list for the sample.

• Randomly choose five classrooms in the school and use all the students in those classrooms for the sample.

• Divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year.

• From a numbered list of all student names, randomly choose a starting point and then choose every tenth student on the list.

• From a randomly chosen home basketball game, choose every tenth student who enters the gymnasium.

Answer explanation

D. Such a method will probably overrepresent fans of basketball and underrepresent other subgroups of students.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

The supervisor of a shopping mall distributed a customer-satisfaction survey by handing it to people as they came through one of the doors to the mall one day. Of those handed out, 220 were completed and returned. Should the results of the survey be generalized to the population of all customers of the shopping mall?

• Yes, because the sample size is large.

• Yes, because only people entering the mall were given the survey.

• Yes, because the sample was representative.

• No, because a random sample from all customers of the shopping mall was not selected.

• No, because not all customers were selected.

Answer explanation

D. It is only appropriate to make generalizations about a population based on samples that are randomly selected from the population. The sample described here is not a random sample, so the results should not be generalized to the population of all customers of the mall.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

Which of the following is a benefit to using a random sample for an observational study?

• The random sample allows for different treatments to be assigned.

• A causal relationship can be determined.

• The results of the observational study can be generalized to the population.

• A random sample is the easiest method of data collection.

• The distribution of the sample will match the distribution of the population.

Answer explanation

C. Random samples are usually representative of the population and results can be generalized.

Tags

CCSS.HSS.IC.B.3

Joshua wants to investigate the opinions of young adults in the country, ages 16 years to 23 years, about time spent playing video games. He plans to administer a survey to a sample of people. Which of the following samples is most likely to generalize to his population of interest?

• A nationwide sample of people ages 16 to 23

• A sample of attendees of a gaming convention

• A sample of people ages 16 to 23 in Joshua’s hometown

• A sample of people who click on a link in an online gaming site

• A sample of people who buy video games from an online store

Answer explanation

A. Such a sample will be most representative of all people in the country in the targeted age-group.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

The owner of a small company needs to collect data on the educational background of all 30 of the company’s employees. Which of the following is the best method to use for data collection?

• A census

• A cluster sample

• A simple random sample

• A stratified sample

• A systematic random sample

Answer explanation

A. Because information is needed on the population of all employees, a census should be taken.

To estimate the size of a typical housing unit in a certain town, a sociologist plans to use a cluster sampling method to gather data. Which of the following describes a cluster sampling method?

• Randomly select a certain number of housing units in the town.

• Divide all housing units into three groups: small, medium, and large. Then randomly select a certain number from each group.

• Divide the town into nonoverlapping regions. Randomly select from the nonoverlapping regions, and select all housing units in those regions.

• Obtain a listing of all housing units currently for sale in the town, and use the size information given in the listing.

• Obtain the records kept by the town of all housing units in the town, and use the information in those records.

Answer explanation

C. Cluster sampling involves dividing the town into nonoverlapping regions, selecting some of the regions at random, and then recording the sizes of the housing units in each of the selected clusters. The nonoverlapping geographic regions are the clusters.

Tags

CCSS.HSS.IC.B.3

A certain company has five departments, A, B, C, D, and E. The number of employees in each department is 10, 10, 20, 30, and 30, respectively. A sample of 10 employees from all employees will be selected. Of the following descriptions of sampling procedures, which is most likely to introduce a potential source of bias?

• Randomly select 10 employees from department C

• Randomly select 10 employees from all 100 employees

• Randomly select 2 employees from each of the five departments

• Randomly select 1 employee from each of A and B, 2 employees from C, and 3 employees from each of D and E

• Randomly select every tenth employee from a randomized list of names of all employees

Answer explanation

A. If the sample consists of employees from department C only, then responses from the department C employees are systematically favored over responses from employees in other departments.

Tags

CCSS.HSS.IC.B.3

A scientist studying soil acidity collected soil samples from a plot of land with a stream running through it. The soil samples came from land located on only one side of the stream. What is the potential source of bias that might result from the sampling method?

• Voluntary response bias

• Undercoverage bias

• Nonresponse bias

• Response Bias, where responses are self-reported

• Response Bias, where the question wording is leading or confusing

Answer explanation

B. A portion of land has been excluded from providing soil samples, so there is undercoverage of the land in the samples collected. The soil acidity in the sample collected by the scientist may not be representative of the soil acidity of the entire plot because of undercoverage bias.

Tags

CCSS.HSS.IC.B.3