3.1 Statistics: Populations, Samples, and Bias

What is nonresponse bias?

• When individuals chosen for a sample don’t respond, leading to bias if these individuals differ from respondents.

• When survey questions are confusing or leading.

• When individuals inaccurately report their own traits.

• When a sample is composed of only volunteers.

Which of the following is NOT a step in performing a simple random sample (SRS)?

• Assign each individual in the population a number

• Use a random number generator to obtain sample numbers

• Sample the individuals whose numbers were generated

• Only select individuals who show symptoms

A teacher posts a poll to his class website. He asks, “Would you prefer to have the quiz on Friday or Monday?” Out of his 32 students, 8 responded to the poll. 62.5% of the respondents indicated they would prefer to have the quiz on Friday. How could bias have impacted the estimate of 62.5%?

• The results may not represent the preferences of all students because only 8 out of 32 responded.

• The results are always accurate if a poll is used.

• The results are not biased because everyone had a chance to respond.

• The results are biased only if the teacher prefers Friday.

A vegetable gardener is trying to determine the average number of pea pods produced by all 24 of their pea pod plants. The plants are growing all around the perimeter of a rectangular garden. The gardener selects 5 plants along one side of the garden, counts the number of pea pods on each plant, and found the mean of these values. How could sampling bias have impacted the sample mean number of pea pods from the 5 plants chosen?

• The sample may not represent all plants if only one side of the garden is chosen.

• Sampling bias does not affect the mean.

• The sample is always representative if 5 plants are chosen.

• The sample mean will always be higher than the population mean.

Suppose we want to estimate the proportion of cars in a parking lot that have a manual transmission rather than an automatic transmission. If the lot has 80 cars, describe how you would implement a simple random sample of 18 cars.

• Assign a number to each car from 1 to 80, then randomly select 18 unique numbers and choose the corresponding cars.

• Select the first 18 cars you see in the parking lot.

• Ask 18 people at random if their car has a manual transmission.

• Choose every fourth car in the parking lot.

The principal is looking to get a representative sample of all students at the high school to gauge their opinion on a new mascot. She takes a simple random sample of students sitting in the cafeteria at lunch. Note: At this school, seniors are allowed to leave campus at lunch. What type of sampling bias is present?

• Undercoverage Bias

• Nonresponse Bias

• Voluntary Response Bias

• Question Wording Bias

A middle school is considering a “no-homework” policy, but first administrators want to know if students are spending an exorbitant amount of time on homework each night. A random sample of middle school students is asked how much time they spend on homework each night on average. What type of sampling bias is present?

• Undercoverage Bias

• Nonresponse Bias

• Voluntary Response Bias

• Self-Reported Response Bias

The owner of a coffee shop is hoping to survey the employees on their opinions of the coffee made at the shop. A simple random sample of 10 employees is selected, and an anonymous survey is emailed to each of them. The owner receives 4 responses. What type of sampling bias is present?

• Undercoverage Bias

• Nonresponse Bias

• Voluntary Response Bias

• Question Wording Bias

Research finds that, in general, the higher an incoming college student scores on a given test, the higher the student's college GPA. Which of the following best describes this relationship?

• A bimodal distribution

• A normal distribution

• A skewed distribution

• A positive correlation

• A negative correlation

Research based on observation of people in any given environment (place) in known as:

• Experimentation

• Participant Research

• Natural Observation

• In-Depth Surveying