I need so help figuring out which statement is true or false.
1. A parameter always describes a larger group than a statistic.
2. The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of all possible sizes from the same population.
3. Statistical inference allows one to find the exact value of a parameter.
1. True. Parameters are data from the total population, while statistics are data from samples.
2. True. A sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). The formula for the sampling distribution depends on the distribution of the population, the statistic being considered, and the sample size used. A more precise formulation would speak of the distribution of the statistic as that for all possible samples of a given size, not just "under repeated sampling". (From <(Broken Link Removed)
3. False. It is an estimate.
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
I'll give you a few hints:
One is true; two are false.
The two false statements are false because of one word in each statement.
Identify the population and the sample:
A survey of 1200 credit card found that the average late fee is $24.3?
To determine which statement is true or false, let's break down each statement and explain them one by one.
1. A parameter always describes a larger group than a statistic.
To understand this statement, we need to grasp the definitions of a parameter and a statistic.
- A parameter is a numerical summary of a population.
- A statistic is a numerical summary of a sample.
In general, a parameter describes the entire population, while a statistic describes a subset of the population (sample). Therefore, statement 1 is generally true. However, there can be exceptions depending on the context or research design being used.
To verify if statement 1 is true or false in a specific scenario, you would need to assess the context and determine if the parameter indeed represents a larger group or if the statistic covers a broader scope than the parameter.
2. The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of all possible sizes from the same population.
This statement describes the concept of the sampling distribution, which is fundamental in statistics.
- The sampling distribution refers to the distribution of a statistic when we repeatedly sample from the same population.
So, statement 2 is true. The sampling distribution of a statistic represents the range of values that the statistic can take in all possible samples of different sizes from the same population.
To understand this concept better, imagine conducting numerous samples of different sizes from the same population, computing a specific statistic (e.g., mean, proportion) for each sample, and then plotting the distribution of these statistics. The resulting distribution is called the sampling distribution of that statistic.
3. Statistical inference allows one to find the exact value of a parameter.
To comprehend this statement, let's clarify the concept of statistical inference.
- Statistical inference involves drawing conclusions or making predictions about a population based on sample data.
The objective of statistical inference is to estimate or make statements about a population by using observed data from a sample. However, it is important to note that statistical inference provides estimates or predictions about parameter values but not the exact values.
Therefore, statement 3 is false. Statistical inference allows us to make probabilistic inferences about parameters, providing estimates within a certain level of accuracy or confidence. It does not yield the exact value of the parameter but rather a range or estimate that is likely to contain the true parameter value.
In summary:
- Statement 1 is generally true, but exceptions may exist.
- Statement 2 is true, as it describes the concept of the sampling distribution.
- Statement 3 is false, as statistical inference provides estimates or predictions, not exact values.