Question

When spending large amounts to purchase advertising time, companies want to know what audience they'll reach. In January \(2007, \mathrm{a}\) poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were looking forward more to the football game or to watching the commercials. Among the men, \(16 \%\) were planning to watch and were looking forward primarily to the commercials. Among women, \(30 \%\) were looking forward primarily to the commercials. a) Was this a stratified sample or a blocked experiment? Explain. b) Was the design of the study appropriate for the advertisers' questions?

Short answer

a) Stratified sample. b) Yes, it is appropriate for advertisers' questions.

Step-by-step solution

Understanding Stratified Sampling

Stratified sampling involves dividing a population into subgroups, or strata, that share similar characteristics and then taking a random sample from each subgroup. In this scenario, the population of interest is American adults, and the subgroups are defined by gender: men and women.

Understanding Blocked Experiment

In a blocked experiment, participants are divided into groups (blocks) that share some characteristic before a treatment is applied to each block. The purpose is to control for variables that could affect the outcome. However, in this scenario, there was no treatment applied; participants were simply surveyed.

Identify the Sampling Method Used

Since the poll divided respondents into gender groups (men and women) and then collected responses from each group without applying treatments, this set-up corresponds to stratified sampling rather than a blocked experiment.

Analyze the Study Design for Appropriateness

The study design appears appropriate for the advertisers' questions as it separates responses by gender, which could provide advertisers with insights into different preferences between men and women regarding commercials. Knowing these preferences can inform advertisers about tailoring their content for specific audiences.

Key concepts

Stratified Sampling

Stratified sampling is a sampling method used to ensure representation from different subgroups within a population. This technique involves dividing the entire population into distinct subgroups, known as strata, based on shared characteristics. In the problem's context, the population is American adults, and the two strata are defined by gender: men and women.

The main advantage of stratified sampling is that it increases precision and enables better comparisons between groups. By ensuring each subgroup or stratum is represented, researchers get a clearer understanding of any differences or similarities between the groups. For example, if advertisers are trying to understand the preferences of men and women regarding Super Bowl commercials, stratified sampling allows them to analyze and compare responses based on gender-specific data.

This method is particularly useful in scenarios where there are notable differences between subgroups, and these differences could impact the results. Stratified sampling reduces the chance of random sampling error and increases confidence in the results. In summary, stratified sampling in the exercise allows advertisers to make gender-based comparisons on advertisement preferences during the Super Bowl.

Blocked Experiment

A blocked experiment is a technique used in experimental design where subjects are divided into groups or 'blocks' based on certain characteristics. The main purpose is to control for variability and isolate the effect of the treatment on the outcome. For example, if the goal is to measure how different treatments affect blood pressure, patients may be blocked by age to ensure age-related differences do not skew results.

In essence, blocking minimizes the effect of confounding variables that could affect the results. The process usually involves two steps: blocking and randomization. First, participants are grouped into blocks that are similar in some specific manner. This ensures any influence those shared characteristics might have on the outcome is controlled across treatments.

However, unlike blocked experiments, the scenario in the exercise does not introduce any treatment to test an effect. Instead, it solely collects survey data from defined groups. Therefore, the advertisement survey is not a blocked experiment because no interaction or manipulation (treatment) is performed. It simply uses gender as a stratum for obtaining responses, which helps classify it as stratified sampling.

Survey Design

Survey design is a crucial aspect of research that directly impacts the quality and applicability of the data collected. In the context of the Super Bowl advertisement survey, designing an effective survey involves several key elements: defining the target population, choosing the right sampling method, and crafting clear, unbiased questions.

Defining the target population is the first step. Here, the goal was to determine how different gender groups perceive Super Bowl commercials. Ensuring that the survey reached a representative demographic helped advertisers obtain reliable insights into audience preferences.

The choice of sampling method is also significant; stratified sampling was utilized to ensure clear insights into gender-specific preferences. By separating respondents into gender groups, the survey design reflects the varied interests between men and women, offering advertisers valuable data.

Additionally, crafting survey questions that are direct and impartial is essential. In this study, questions needed to elicit genuine responses regarding preferences for watching football or commercials. Ensuring clarity in questions and consistency in data collection across groups enhances the quality and applicability of results, making the survey a fitting tool for advertisers to tailor their strategies based on gender-specific interests.