In an online survey about shopping habits, the following question was posted:

"Do you often shop online?"

A total of 120,456 individuals responded, among them, 70% said "yes". What is this type of survey called, where the people surveyed are only those who chose to participate? What is problematic with this sampling method?

The following are recorded temperatures (in °F) at noon in different cities on a particular day:

$\text{72 85 90 78 88 76 84 91 79 82 87 80}$

Are the temperature values discrete or continuous data?

For the multiple regression equation developed to predict fuel efficiency (in $\text{mpg}$) of cars based on their engine size (in $\text{L}$), vehicle weight (in $\text{kg}$), and horsepower, the linear correlation coefficient ($r$) was found to be $r=-0.803$.

(i) What is the value of the coefficient of determination ($R^2$)?

(ii) What practical information does the coefficient of determination give in this context?

Favorite ice cream flavor among vanilla, chocolate, and strawberry is best described as which level of measurement?

A team member reports weekly hours: [32, 40, 48, 56]. Compute the mean and state whether multiplying the mean by 1.5 to plan staffing is a valid operation. Show calculations.

A dataset records classroom temperatures in Fahrenheit. The analyst converts them to Kelvin before applying a multiplicative model that assumes ratios of temperatures are meaningful. Critically evaluate whether this modeling assumption is justified.

Identify the population, sample, and the sample data set.

A poll of $300$ households in a city found that $20\%$ planned to install solar panels within the next year.

A researcher wants to test the effectiveness of a new medication. She assigns participants to two groups. Only the participants do not know whether they are receiving the medication or a placebo, but the researcher does. What type of experiment is this?

Imagine you are polling for a statewide referendum. How would you design your sampling strategy? Explain the distinction between 'registered voters' and 'actual participants.' What is the purpose of stratification in your sampling plan?

Why is it more practical to use a sample instead of an entire population when conducting a study?

A public health agency has a roster of all $\mathrm{250,000}$ households in a city and plans to select a systematic sample of $200$ households to inspect. Determine the sampling interval, $k$.

Suppose the intracluster correlation is small. Which of the following statements is correct about cluster sampling efficiency for a fixed total sample size? Select the best answer.