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Chapter 1: Problem 6

a. Distinguish between description and inference as reasons for using statistics. Illustrate the distinction using an example. b. You have data for a population, such as obtained in a census. Explain why descriptive statistics are helpful but inferential statistics are not needed.

Short Answer

Expert verified
Descriptive statistics summarize and organize data, while inferential statistics draw conclusions from samples. In a census, inferential statistics aren't needed because the entire population data is already available.

Step by step solution

01

Understanding Descriptive Statistics

Descriptive statistics summarizes data from a population or sample using measures such as mean, median, mode, standard deviation, etc. It provides a way to quickly understand the basic characteristics of the data without drawing further conclusions.
02

Understanding Inferential Statistics

Inferential statistics involve drawing conclusions about a population based on a sample. It uses methods such as hypothesis testing and confidence intervals to infer characteristics about a population, estimation beyond the immediate data.
03

Differentiating Description and Inference

Description is using statistics to describe data, while inference is using statistics to make predictions or decisions about a population based on a sample. For example, if you surveyed the height of students in a class, descriptive stats could tell you the average height, while inferential stats might estimate the average height of all students in the school.
04

Using Descriptive Statistics in Census

Descriptive statistics are vital in a census as they provide a clear overview of the population data. It helps to organize and summarize the vast amount of data, making it manageable and understandable.
05

Why Inferential Statistics Are Not Needed in a Census

Inferential statistics are unnecessary in a census because a census already includes the entire population data. Since there is no need to infer from a sample about a population, inference operations are redundant.

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Key Concepts

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

Descriptive Statistics
Descriptive statistics is all about simplifying complex data sets to make them more understandable.
By calculating measures like the mean, median, and mode, you can summarize data into easily digestible chunks.
These statistics provide a snapshot of your data. Whether it's the average test score of a class or the standard deviation of weights in a group, descriptive statistics answer the 'what is' question.
  • Mean: The average value of a data set.
  • Median: The middle value when the data set is organized in order.
  • Mode: The most frequently occurring value in the data set.
By using these tools, descriptive statistics eliminate the need for examining each data point individually. It's like summarizing a book into a brief summary 鈥� you get the essence without the need to read each page.
Inferential Statistics
Inferential statistics go a step further by allowing us to make predictions or decisions about a larger group based on a sample.
They are like using past weather patterns to forecast future conditions. The tools here include hypothesis testing, regression analysis, and confidence intervals.
  • Hypothesis Testing: A method to test an assumption regarding a parameter.
  • Confidence Intervals: A range of values that is likely to contain the population parameter.
  • Regression Analysis: A way to predict the value of one variable based on the value of another.
These statistical methods are essential when working with samples because they allow us to draw conclusions about larger populations.
It's like taking a tiny spoonful of soup to predict the taste of the whole pot.
Census Data
Census data offers a comprehensive collection of information about every individual in a population.
Since it covers the entire group, there's no guesswork needed.
With such exhaustive data, descriptive statistics become incredibly helpful.
They enable us to create a clear picture by organizing and summarizing without the need for inference.
  • Provides the actual data, eliminating sampling error.
  • Helps in planning, policy-making, and research with an accurate portrayal of population characteristics.
  • Allows detailed demographic analysis simply through descriptive measures.
When you have a full scoop of the entire pot, every detail of the population is readily available, making inferential statistics redundant.
Statistical Inference
Statistical inference comes into play when we need to make informed assumptions about a population based on a sample.
Unlike a census, where all data is present, statistical inference allows us to fill in the gaps.
By using techniques like sampling distribution and test of significance, we can logically infer unknowns for a whole group.
  • Sampling Distribution: The distribution of sample statistics to make inferences about the population parameter.
  • Test of Significance: Determines the probability that an observed difference could have occurred just by random chance.
These tools enable us to estimate the world beyond our immediate dataset.
Think of it as making educated guesses based on the evidence at hand. Statistical inference guides us in making predictions, checking models, and testing theories, offering insights that aren't immediately obvious from the data itself.

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Most popular questions from this chapter

A poll was conducted by Ipsos Public Affairs for Global News. It was conducted between May 18 and May \(20,2016,\) with a sample of 1005 Canadians. It was found \(73 \%\) of the respondents "agree" that the Liberals should not make any changes to the country's voting system without a national referendum first. (http://globalnews.ca/news/). Find the approximate margin of error if the poll had been based on a sample of size (a) \(n=900,\) (b) \(n=1600,\) and \((\mathrm{c}) n=2500 .\) Explain how the margin of error changes as \(n\) increases.

Suppose a student is interested in knowing the preferred holiday destinations of the faculty members in his university. He is affiliated to the college of business and interviews a few of the faculty members of this college about their preferred holiday destination. In this context, identify the (a) subject, (b) sample, and (c) population.

The Voice of the People poll asks a random sample of citizens from different countries around the world their opinion about global issues. Included in the list of questions is whether they feel that globalization helps their country. The reported results were combined by regions. In the most recent poll, \(74 \%\) of Africans felt globalization helps their country, whereas \(38 \%\) of North Americans believe it helps their country. (a) Identify the samples and the populations. (b) Are these percentages sample statistics or population parameters? Explain your answer.

Mobile data costs \(\quad\) A study is conducted by the Australian Communications and Media Authority. Based on a small sample of 19 mobile communications plans offered, the average cost per \(1000 \mathrm{MB}\) of free monthly mobile data allowance is found to be \(\$ 5.40,\) with a margin of error of \(\$ 2.16 .\) Explain how this margin of error provides an inferential statistical analysis.

The Institute for Public Opinion Research at Florida International University has conducted the FIU/Florida Poll (www2 .fiu.edu/orgs/ipor/globwarm2.htm) of about 1200 Floridians annually since 1988 to track opinions on a wide variety of issues. In 2006 the poll asked, "How concerned are you about the problem of global warming?" The possible responses were very concerned, somewhat concerned, not very concerned, and haven't heard about it. The poll reported percentages (44,30,21,6) in these categories. a. Identify the sample and the population. b. Are the percentages quoted statistics or parameters? Why?
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