Question 1

A researcher wants to study the effect of a new medication on blood pressure. She divides the population into age groups (20-29, 30-39, 40-49, etc.) and randomly selects participants from each group. Which sampling method is she using?

Accepted Answer

Stratified sampling

Question 2

In a normal distribution, what percentage of data falls within two standard deviations of the mean?

Accepted Answer

$$95\%$$

Question 3

A city is divided into 10 districts. A researcher randomly selects 3 districts and surveys all residents in those districts. What sampling method is this?

Accepted Answer

Cluster sampling

Question 4

Which formula represents the regression line in the context of predicting $$y$$ from $$x$$?

Accepted Answer

$$\hat{y} = b_1x + b_0$

Question 5

A researcher selects every 5th person from a list of hospital patients to participate in a survey. Which sampling method is being used?

Accepted Answer

Systematic sampling

Question 6

In the context of regression analysis, what does the unexplained deviation $$y - \hat{y}$$ represent?

Accepted Answer

The difference between the observed value and the predicted value

Question 7

A study finds that seniors who get flu shots are 27% less likely to be hospitalized for pneumonia or influenza. What type of study design is this most likely to be?

Accepted Answer

Observational study

Question 8

If a data set is normally distributed with mean $$\mu$$ and standard deviation $$\sigma$$, what is the probability that a randomly selected value is greater than $$\mu + 2\sigma$$?

Accepted Answer

$$2.5\%$$

Question 9

Which of the following best describes the purpose of stratified sampling?

Accepted Answer

To ensure that subgroups of a population are represented proportionally in the sample

Question 10

A researcher wants to estimate the average commute time for all employees in a large company. She randomly selects 50 employees from the entire company. Which sampling method is this?

Accepted Answer

Simple random sampling

Question 11

In the context of the normal distribution, what is the range that contains approximately $$99.7\% of $$the data?

Accepted Answer

$$\mu - 3\sigma to$$ $$\mu + 3\sigma$$

Question 12

Which of the following is a potential source of bias in the influenza vaccine study described in the materials?

Accepted Answer

Participants self-selected whether to get the vaccine

Question 13

If the total deviation in regression is $$y - \bar{y}$$, and the explained deviation is $$\hat{y} - \bar{y}$$, what is the unexplained deviation?

Accepted Answer

$$y - \hat{y}$$

Question 14

A researcher wants to ensure that every possible sample of a given size has an equal chance of being selected from the population. Which sampling method should she use?

Accepted Answer

Simple random sampling

Question 15

Which of the following statements about the empirical rule is correct?

Accepted Answer

Approximately $$68\% of $$data falls within one standard deviation of the mean

Question 16

In regression analysis, what does the explained deviation $$\hat{y} - \bar{y}$$ represent?

Accepted Answer

The part of the total deviation accounted for by the regression model

Study Notes: Data Collection, Sampling Methods, and Statistical Analysis in Introductory Statistics

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