Complete all Questions, and submit final documents in PDF form on Canvas.

The Data

Gallup is an organization that conducts extensive polls aimed at exploring a variety of facets about societal opinions, political views, and more. In December of 2017, the Gallup organization released an article called The 2017 Update on Americans and Religion. The article explored the relationship between religion and political party, the degree to which Americans considered themselves religious as well as the proportion of Americans identifying with particular religions. In this lab, we are going to use the survey results to explore changes in how Americans self-identify when it comes to their religious beliefs.

While we usually start our process with EDA, in this case, Gallup has done this work for us. Accordingly, we are going to begin by taking a look at the article and using it to answer the following questions. This means you have to open the article and take a look to find the answers to the questions below.

  1. What is the population of interest for this survey?
  2. How many people were interviewed for this survey, i.e., what is the sample size?
  3. Which of methods were used to gather information?

    A) Face to face
    B) Telephone
    C) Internet
    D) All of the above

  4. According to the survey, what proportion of Americans in 2017 identified themselves as highly religious?
  5. Is this value a sample statistic or population parameter?

Early in this course, we talked about the need to confirm the reliability of your data before using it to make any conclusions. One thing to look for to assess the validity of supplied data is information like margins of error, sampling methods, and sample sizes. If this information is provided, this lends more support to the claim that the data presented can be safely used. It also allows us to assess any potential biases that may result from the data collection methods.

  1. Based on the collection technique for this Gallup poll, what is one potential source of bias?

Inference with a single proportion

The Gallup poll provides sample statistics, that is, calculations made from the sample. We are more interested in what information this sample can provide us about population parameters. Based on the survey results, we are able to determine what proportion of people in the sample reported being highly religious. Our goal is to estimate the proportion of adults in the United States who would report being highly religious. As we have done for population means, we are going to use confidence intervals and hypothesis tests to take information from the sample and make conclusions about the population.

  1. Write out the conditions for inference that we need to check before constructing a 95% confidence interval for the proportion of adults in the United States in 2017 who identify as highly religious. Are you confident that all of the necessary conditions are met? Explain.
    1. What is the standard error associated with the point estimate \(\hat{p}\) we would use for building a confidence interval?
    1. Construct and interpret a 95% confidence interval for the proportion of American adults who identified as highly religious in 2017.
    1. Why do you think the margin of error is so small?
    1. Using a significance level of .05, conduct a hypothesis test to see if the proportion of American adults who identified as highly religious in 2017 was less than .4, or 40%. Write down all 6 steps, and state your conclusion clearly in context of the data in Step 6. Note: In Step 4, just state the distribution; you do not need to draw a picture. To produce the necessary mathematical notation for the 6 steps, copy and paste the following into the white space in your Markdown.

      Step 1: $H_0: , H_a:$

      Step 2: $\bar{x} = , SE=$

      Step 3:

      Step 4: Assuming all conditions are met,if the null hypothesis were true, the sampling distribution of the test statistic is a ? distribution.

      Step 5: The p-value is ?. This means that ...

      Step 6:

    This lab was written by Dr. Nicole Dalzell at Wake Forest University. It is released under a Creative Commons Attribution-ShareAlike 3.0 Unported.