Ch. 1 Homework Pt. 2 – Flashcards
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A news service conducted a survey of 1004 adults ages 18 years or older in a certain country, August 31 - September 2, 2015. The respondents were asked, "Of every tax dollar that goes to the federal government, how many cents of each dollar would you say are wasted?" Of the 1004 individuals surveyed, 34% indicated that 51 cents or more is wasted. The news service reported that 34% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 3% and a 90% level of confidence. Complete parts (a) through (e) below:
(a) What is the research objectives?
(b) What is the population?
(c) What is the sample?
(d) List the descriptive statistics
answer
(a)
[[--To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar]]
(b)
[[--Adults in the country aged 18 years or older]]
(c)
[[-- the 1004 adults in the country that were surveyed]]
(d)
[[-- 34% of the individuals surveyed indicated that 51 cents or more is wasted]]
(e)
[[-- The news service is 90% confident that the percentage of all adults in the country who believe the federal government wastes 51 cents or more of every dollar received is between 31% and 37%]]
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How do you correctly infer results from a statistical study onto a population with 90% confidence of a 3% margin of error on a 34% statistical figure?
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with 34%, there would be a 90% confidence level that the statistical figure is in between 31% and 37%
- the margin of error can usually be either greater or smaller than originally expected, and they are 90% confident in that range for the studied statistic
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What are descriptive statistics?
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organizing and summarizing the data, describing the data through summaries, tables and graphs.
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It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed ion the data. For example, if a researcher wanted to describe countries based on ISBN (International Standard Book Number) group identifier, what level of measurement would be variable " ISBN group identifier" be? Now suppose the researcher felt that certain countries with greater populations received higher identifying numbers. Does the level of measurement of the variable change? if so, how?
(a) What is the level of measurement of the variable "ISBN group identifier" in the original scenario?
(b) Does the level of measurement of the variable change in the second scenario?
answer
(a) nominal
Because "ISBN group identifiers" is only one number per country, You cant rank each identifier as being better than the other or that there's more of them, because it's just a group identifier, not a group measure. Usually only 1 number per country.
(b) Yes, it changes to ordinal
Because by assigning higher group identifiers to countries with higher population, you're adding another category of data whose function is to order and organize country according to population. Therefore, categorical with numerical ranking.
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Define variability and how it affects the analysis of statistics?
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Def- difference in the results of different studies even under similar circumstances.
Variability affects how reproducible and testable the statistic is. For example, if you go to a dog park on any given day and record different dog sizes, every day could bring different dog breeds, and every day could result in different data. Making your given statistic becomes harder to reproduce. Repeat the experiment at a day care, and the differences in condition wouldn't result in major statistical analysis differences.
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What does the saying "data vary" mean and how does variability affect the results of statistical analysis?
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"Data vary" means that the values of the variable change form individual to individual. In addition, certain variable scan change over time for certain individuals. Because data vary, two different statistical analysis of the same variable can lead to different results.
Individuals are different from each other, even if they are similar, you cant be 100% alike someone else, regarding most things in your life.
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What is an observational study, and can it determine causation?
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Observing and recording data without influence. measures the response variable without trying to influence and control either the response, or explanatory variable.
*Cannot claim causation between an explanatory variable and a response variable because it could not influence or control either one to determine which caused what.
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What's a designed experiment and can it determine causation?
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Researcher assigns the individuals in a study to a certain group, and intentionally changes the vale of an explanatory variable, and then records the value of the response variable in each group.
*Can determine causation between an explanatory variable and a response variable
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What is the response variable?
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weather or not what we are trying to study happened?
e.g. in an experiment of whether or not radio waves cause brain tumors, whether or not brain tumors were contracted would be the response variable
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Whats a cross sectional study?
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It's an observational study that collects info at a specific point in time or over a short period.
an advantage of cross-sectional studies is that they are cheap and quick to do, however limited on long term results, on weather or not something changed after the initial cross-sectional study was performed.
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What is a case-control study?
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an observational study that is retrospective, and individuals will be organized into homogeneous groups (similar characteristics and demographics) and asked about events in the past, and answers will be compared with homogeneous groups with opposite explanatory variables, like smokers compared with non-smokers.
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What is a cohort study?
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these are prospective observational studies, meaning they look towards the future over a long period of observation. The studied individual will naturally get exposed to other variables (not intentionally by the researcher's hand) and then at the end of the study period the values of the response variables would be recorded. This is the most powerful and comprehensive form of observational studies.
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Simple Random sample
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take a simple size n ("lower case + sample, upper case is population) from a large population size N, where every possible simple size n has an equally likely chance of occurring to every other possible size n
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Stratified Sample
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separate population into non-overlapping groups and THEN obtain a simple sample of each group. (first separate into non-overlapping groups, then simple sample)
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Systematic Sample
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Select every Kth individual from a population, starting with the first 3rd individual etc. between on and K. Like randomly selecting every forth customer at a grocery line to take a serving starting after the first 5th, random selection with a structured format.
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Cluster sample
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selecting all individuals within a randomly selected collection or group of individuals. So selecting a randomly selected cluster unit, like certain random online classes, and collecting data on ALL of the population of that randomly selected cluster
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Convenience sample
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When individuals in a sample were easily obtained not based on any element of randomness but by ease of access to the researcher.
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Inferences based on voluntary response samples are generally not reliable because
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It is often the case that individuals who volunteer do not accurately represent the population.
e.g. because the certain volunteers who respond, might have very strong feelings either way, or not truly belong in the studied population. All of which introduces bias.
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When are populations under-represented?
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when it's proportionally smaller in a sample than it truly is in the population
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Bias def.
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When the results of a sample are not representative of the population or it's true feelings
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Sample bias
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when the method used for selection, tends to favor certain individuals
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Non-response bias
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individual selected to be in the sample who do not respond feel differently from those who do respond
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Response bias
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when answers in a study or survey don't reflect the true feelings of the respondents
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non-sampling errors
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result from undercovery, non-response bias, response bias, or data entry errors
