Question

Locate the results of a recent survey that show at least two variables in a newspaper, magazine, or internet article. Outline the survey data so that your peers can understand the variables and results. Then identify at least one key statistical inference formula involving two of more parameters that you could use to evaluate the data. Provide a brief explanation of why you selected the formula you did and why it matters. Also, explain what the formula is and where it is in the textbook and clearly define your parameters. Do not use regression or correlation examples since we will cover them during the next module.

Be sure to support your statements with logic and argument, citing any sources referenced.

Answer 1

The Pew Research Center published a survey named ‘Libraries at the Crossroads’ on September 15, 2015.

This survey focuses on the use of libraries by the general American population and how they view libraries in the present context. Below is an outline of the survey data and some key aspects studied in the survey:

• New program possibilities that citizens expect that libraries should offer
• Percentage of Americans who use a library, analyzed over time.
• Purpose of usage of libraries and the perceived impact of libraries.
• Effect of gender and level of education on usage of libraries.
• Effect of demographics on the usage of electronic interfaces of libraries.
• Effect of libraries on communities.
• Effect of demographics on the perceived impact of libraries.

A probability sample of 2004 individuals representing the national population was collected. The responses provided by these individuals were corrected for known biases and then analyzed.

One key formula that is used to evaluate the data is the standard error of the sample statistics that are used to define the confidence intervals for these statistics.
     The standard error is given by (d. eff.)^1/2 * [p(1 - p)/n]^1/2
          where, d. eff. = the design effect
                        [p(1 - p)/n]^1/2 is the general formula for the standard error of a sample proportion

Certain post-data collection statistical adjustments are applied to the data to account for known biases. This requires analysis procedures that are different from simple random sampling. The effects of these design features need to be incorporated into tests of statistical significance when using this data. Therefore, the so-called ‘design effect’ is used to adjust the standard error of the sample proportion.