91Ó°ÊÓ

Influencing Voters: Is a Phone Call More Effective? Suppose, as in Exercise \(4.37,\) that we wish to compare methods of influencing voters to support a particular candidate, but in this case we are specifically interested in testing whether a phone call is more effective than a flyer. Suppose also that our random sample consists of only 200 voters, with 100 chosen at random to get the flyer and the rest getting a phone call. (a) State the null and alternative hypotheses in this situation. (b) Display in a two-way table possible sample results that would offer clear evidence that the phone call is more effective. (c) Display in a two-way table possible sample results that offer no evidence at all that the phone call is more effective. (d) Display in a two-way table possible sample results for which the outcome is not clear: There is some evidence in the sample that the phone call is more effective but it is possibly only due to random chance and likely not strong enough to generalize to the population.

Step by step solution

01

Define the null and alternative hypothesis

(a) The Null Hypothesis(H0): The phone call is as effective as the flyer. The Alternative Hypothesis(H1): The phone call is more effective than the flyer.

02

Display a two-way table suggesting the phone call is more effective

(b) Assume out of 100 voters who received the flyer, 40 decide to support the candidate. Out of the 100 who received a phone call, 70 decide to support. This can be displayed in a two-way table as follows:\[\begin{tabular}{|c|c|c|c|}\hline& Support & No Support & Total \\hlineFlyer & 40 & 60 & 100 \\hlinePhone Call & 70 & 30 & 100 \\hlineTotal & 110 & 90 & 200 \\hline\end{tabular}\]This indicates that the phone call is more effective than the flyer.

03

Display a two-way table offering no evidence the phone call is more effective

(c) Assume that out of 100 voters who received either method, 50 decide to support the candidate. This can be displayed in a two-way table as follows:\[\begin{tabular}{|c|c|c|c|}\hline& Support & No Support & Total \\hlineFlyer & 50 & 50 & 100 \\hlinePhone Call & 50 & 50 & 100 \\hlineTotal & 100 & 100 & 200 \\hline\end{tabular}\]This indicates that both methods are equally effective.

04

Display a two-way table where the outcome is unclear

(d) Assume out of 100 voters who received the flyer, 40 decide to support the candidate. Out of the 100 who received a phone call, 55 decide to support the candidate. This can be displayed in a two-way table as follows:\[\begin{tabular}{|c|c|c|c|}\hline& Support & No Support & Total \\hlineFlyer & 40 & 60 & 100 \\hlinePhone Call & 55 & 45 & 100 \\hlineTotal & 95 & 105 & 200 \\hline\end{tabular}\]This situation is unclear- the phone call seems more effective, but not by a large margin. This could be just due to random chance and might not be strong enough evidence to generalize to the population.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Null and Alternative Hypotheses

In the realm of hypothesis testing in statistics, the core of any analysis begins with the definition of two contrasting propositions: the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\text{ or }H_a\)). Understanding these hypotheses is crucial to analyze statistical evidence.

The null hypothesis typically represents a default position or the status quo. It is the hypothesis that there is no effect or no difference in the context of the research. In the scenario with voters, the null hypothesis is asserting that a phone call has the same effectiveness as a flyer in influencing voters to support a candidate.

Conversely, the alternative hypothesis represents the assertion that there is an effect, or there is a difference. It challenges the status quo. In our example, the alternative hypothesis posits that a phone call is more effective than a flyer. It’s worth noting that these hypotheses should be stated before any data collection or analysis to prevent biased interpretations of the results.

Two-way Tables

Two-way tables, also known as contingency tables, are a powerful tool for organizing data in order to analyze categorical variables. They display the frequency distribution of variables and reveal the relationship between them.

In testing our voter influence hypothesis, two-way tables are used to segregate the voters into groups based on the method they were approached with (flyer or phone call) and whether they supported the candidate or not. This arrangement helps to quickly visualize the effectiveness of each method. For clarity, the two-way table should have a disciplined layout, with each row representing a method and each column representing the level of support, culminating in a clearly defined total for each category.

Statistical Evidence

Statistical evidence refers to the data that supports or refutes a hypothesis. This is typically evaluated through measures such as p-values and confidence intervals, which aid in understanding the strength and significance of the evidence.

In the voter influence study, the statistical evidence would be the observed proportion of voters supporting the candidate after receiving either a flyer or a phone call. High statistical evidence against the null hypothesis would be reflected by a significantly higher proportion of supporters with phone calls compared to flyers, suggesting a real effect rather than just a random occurrence.

Random Sampling

A fundamental principle of statistical inference is random sampling, which is essential in obtaining a representative sample of the broader population. The strength and reliability of inferences made from samples to populations depend on the randomness of the sample selection.

For our voting methods exercise, random sampling involves selecting the 200 voters in such a way that each voter has an equal chance of being included in the study. This process minimizes biases and ensures that the results can be generalized to all voters. When a sample is not random, it can lead to misleading conclusions, as it may not accurately represent the population.

Voter Influence Methods

Voter influence methods are the strategies employed to sway voters towards a certain candidate or decision. The comparison of these methods often relies on understanding which tactic is more effective, which is precisely what our current statistical exercise aims to assess.

Different methods can include personal contact like phone calls, sending out flyers, social media campaigns, door-to-door canvassing, or television adverts. Each method comes with varying costs, efforts, and impacts. In this scenario, we focus on phone calls versus flyers. Understanding their respective effectiveness can allow campaign teams to allocate resources efficiently and maximize their impact on voter decisions.