Math Tools Chapter 5-8

By Laura Smith

November 24, 2008

 Chapter 5-Polls and Surveys

Understanding polls and surveys are very useful tools for journalists when reporting about politics or consumer marketing. They offer public opinion but also run the risk of getting skewed one way or another. Therefore, it is the job of the reporter to help the reader understand the polls or survey.

According to Wickham in Math Tools for Journalists, “polls are an estimate of public opinion on a single topic or question.” They are most often used in politics and are based on a sample of the population. Polls can be evaluated on something called random selection. Random selection is when every person in the population being studied has an equal opportunity to be selected.

In selecting samples, there are 6 different ways to look at this. First, there is a census, which is sampling that involves sampling everyone in the population being studied. Next, cluster sampling is sampling in one area or region identified by ZIP codes, counties, or other defined areas. Multistage sampling is next. This is often used in national samples and involves selecting a specific geographic area and randomly selecting sub groups.

Next, there is systematic random. This requires selecting a specific number (like 10) and using a reference book to poll every 10th person. Quota sampling is next and this selects the sample based on known demographic characteristics. Finally, there is probability sampling. This involves putting all of the potential subjects in a hat and drawing out a designated percentage.

Margin of error is also involved in polls and surveys. According to Wickham, margin of error, “indicates the degree of accuracy of the research based on standard norms.” It is expressed as a percentage and is based on the size of a randomly selected sample.

Next, there is confidence level. This is the level or percentage that researchers have confidence in their results of the research they are doing. It usually falls at 90, 95, or 98 percent. It is also closely related to the margin of error.

Next, there are adjusted figures. These are figures that are statistically manipulated to compensate for missing data. Finally, there are z scores and t scores. A z score is also called a standard score and it shows how much a particular figure differs from the average, or mean. In it, the standard deviation is used as the unit measure.  The formula for a z score is (Raw score-mean) / standard deviation. A t score is closely related to a z score and is used when the sample size is small, around 100 or less.

 

Sample Problems

Chapter 5

A few months ago, two presidential candidates, John McCain and Barack Obama debated on the controversial issue of the War in Iraq. At a debate in Tennessee, with a crowd of 5,000 people, McCain received support from 41 percent of the population and Obama receive support from 59 percent. Is Obama leading?

            Yes, because the margin of error for 5,000 people at the 95% level is 1.4. Support could range from 60.4 (59+1.4) to 57.6 (59-1.4). The support for McCain could range from 42.8 (41+1.8) to 39.2 (41-1.8)

Chapter 6

Susy Smith sells books at her store downtown. She pays $10.95 for each book and sells them for $15.00. What is her gross margin?

15.00-10.95=$4.05

If the margin is $4.05 and she sells 10 in one day, what is her gross profit?

4.05 x 10 = $40.50

Chapter 7

Bob paid $900 for a $15,000 bond with a 5 percent interest rate. What is his current yield?

(5% x $1,500) / $900 =8.3%

Chapter 8

A house in Burlington, NC offers a credit of $30,000 and it sets the assessed value at 85% of appraised value. Cindy lives at a house down the street that is appraised at $80,000. What is the assessed value of the house?

($80,000-$30,000) x 0.85 = $42,500

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