Objectives

  1. Differentiate between a population and a sample
  2. Differentiate between a parameter and a statistic
  3. Define and analyze the relationship between explanatory and response variables as well as their role in statistical investigation
  4. Ask questions regarding the associations between variables

Key vocabulary

  1. A population is the entire group of objects a researcher is asking questions about.
  2. A sample is a small percentage of the population which a researcher uses to analyze the parent population.
  3. A parameter is a number which describes some characteristic of the population. For example, the mean age of all men in the US is an example of a population parameter.
  4. A statistic is an estimate of the population parameter which is calculated using the sample.

Case studies

Case study 1: Solar flares and cell mutations

A solar flare is a brief eruption of high energy radiation that is emmitted from the surface of the sun. In a recent study published in The Journal of Geophysical Research scientists wonderd if solar flares were associated with human cell mutations. They collected data on several cell samples collected during solar flare periods. They then calculated the percent of cells that experienced a mutation. They found the solar flare cells had more mutations than the cells cultured during a lack of solar flare.

  • What is the population of interest in this study?
  • What is the population parameter of interest?
  • What is the sample in this study?
  • What was the statistic that the researchers calculated from the sample?

Case study 2: Reusable shopping bags and junk food

In a recent study published in The Journal of Marketing, researchers wondered if using reusable shopping bags made grocery store shoppers more likely to buy junk food (as a percent of their total expenditures). They collected data on thousands of customer purchases at a California super market between 2005 and 2007. They calculated the proportion of a shopper’s total reciept that was due to junk food purchases and found that using a recyclable bag made shoppers more likely to purchase junk food.

  • What is the research question in this study?
  • What is the population of interest in this study?
  • What is the parameter of interest in this study?
  • What is the sample in this study?
  • What was the statistic that the researchers calculated from the sample?

Case study 3: Marijuana, alcohol, and driving

A recent study investigated whether people who drink alcohol and smoke cannibas are more likely to have impaired driving than if they had just consumed either substance. The researchers selected a sample of 18 people and collected data on their gender and age. Then the researchers broke the sample into four groups: those who consumed nothing, those who consumed only alcohol, those who consumed only cannibas, and those who consumed both substances. The researchers then had the study participants drive a virtual car and calcualted the car’s average deviation from the lane. The researchers found that those who had consumed both substances had a larger average deviation than those who only consumed either alcohol or cannibas. However those who consumed only cannibas had smaller average deviations than those who had alcohol impairment.

  • What is the research question in this study?
  • What is the population of interest?
  • What is the sample in this study?
  • What is the population parameter of interest?
  • What is the statistic the researchers calculated in each group?
  • What are the observations?
  • What are the variables?

Case Study 4: College students, E-cigs, and hookah

Recently, researchers published an article in the Public Health Education Journal. They collected data from 2,871 smoking and non-smoking young adults. They were interested in investigating whether this age group saw smoking hookah and E-cigarettes as safer than smoking cigarettes. They calculated the percentage of this group that found hookah and E-cigarettes to be ‘safer than cigarettes’ and found this to be 62.1%.

  • What is the research question being asked in this study?
  • What is the population of interest?
  • What is the population parameter of interest?
  • What is the sample the researchers used the make inferences about the population?
  • What is the statistic the researchers calculated from their sample?

Case study 5: Are more expensive cars heavier?

## Please visit openintro.org for free statistics materials
## 
## Attaching package: 'openintro'
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## The following object is masked from 'package:datasets':
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##     cars

Take a look at the plot above which plots the weights and prices of 54 randomly chosen cars, then answer the following questions.

  • Does there seem to be an association between a car’s price and its weight?
  • If there is an association, is it positive or negative?
  • Do you think that a car’s price causes it to be heavy?

Case study 6: The space shuttle Challenger

On January 28th, 1986 the space shuttle Challenger exploded 2 minutes after launch. While many people know this story, what many people do not know is that a NASA engineer named Allan McDonald had refused to sign the order to launch the space shuttle beacuse he believed that the O-rings which prevented the solid hydrogen rockets from leaking could not withstand the low temperatures forecasted the next morning. Below is a scatter plot displaying data from 23 previous space shuttle launches. Each point on the plot compares the temperature for a space shuttle launch with the corresponding amount of damage of the O-rings for that flight.

  • Based on the plot above does it seem like there is an association between the temperature at launch and the amount of damage the O-Rings sustained?
  • If there is an association, is it positive or negative?
  • Would you have signed the launch order given this data? Or would you have suggested that NASA wait for warmer temperatures to launch?

Case study 7: Is a student’s giftedness associated with parent IQ?

Is giftedness hereditary? In other words do smart parents have smart children? The two plots below show data from a British study investiagting this very question. The first graph is a scatter plot comparing a student’s giftedness score compared with their father’s IQ. The second graph is a scatter plot comparing a student’s giftedness score with their mother’s iq. Examine the plots and answer the questions below them.

  • Does there seem to be an association between a child’s intelligence and their father’s IQ?
  • If there is an association, is it positive or negative?

  • Does there seem to be an association between a child’s intelligence and their mother’s IQ?
  • If there is an association, is it positive or negative?
  • Do you think a child’s giftedness is linked with how intelligent their parents are? Why or why not?