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Will all random samples from a given population have the same mean?
Jaylene123
Data from random samples will not always include the same values. Values are chosen randomly and they may or may not be the same. So means will vary among random samples.
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∙ 7y ago
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What does simple random sample mean in statistics?
It means that every member of the population has the same probability of being included in the sample.
Why is average called the measure of central tendency?
Because, whatever the underlying distribution, as more and more samples are taken from ANY population, the average of those samples will have a standard normal distribution whose mean will be their average. The normal (or Gaussian) distribution is symmetric and so its mean lies at the centre of the probability distribution.
What statistic is produced when the difference between a score and the mean is divided by the standard deviation?
a "T" or a "Z" score. A "T" Score if comparing a sample. A "Z" Score when comparing a population. Remember, a population includes all observation, and a sample includes only a random selection of the population.
What does it mean when the standard error value is smaller than the standard deviation?
It simply means that you have a sample with a smaller variation than the population itself. In the case of random sample, it is possible.
What is circular systematic sampling?
Circular systematic sampling is a random sampling method. An example is random sampling of households. Assume that a random number generator provides the number 49 as a starting point. Starting with the household that is 49 on the target list, every nth household on the list would be sampled until the desired sample size is reached
Why is the central limit theorem an important idea for dealing with a population not normally distributed?
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
What does random sample mean in math?
It is a scheme for selecting a subset from a large population of units in such a way that each unit has the same probability of being included in the sample. Equivalently, it is a scheme whereby all possible samples of a given size have the same probability of being used.
The standard error of the mean is the standard deviation of the sampling distribution of the sample mean?
a large number of samples of size 50 were selected at random from a normal population with mean and variance.The mean and standard error of the sampling distribution of the sample mean were obtain 2500 and 4 respectivly.Find the mean and varince of the population?
What is the difference between Large and small sample?
0.7.1 Difference between Small and Large Samples:-Though it is difficult t draw a clear-cut line of demarcation between large and small samples it is normally agreed amongst statisticians that a sample is to be recorded as large only if its size exceeds 30. The tests of significance used for dealing with problems samples for the reason that the assumptions that we make in case of large samples do not hold good for small samples.The assumption made while dealing with problems relating to large samples are:-(i) The random sampling distribution of a statistic is approximately normal. and(ii) Values given by the samples are sufficiently close to the population value and can be used in its place for calculating the standard error of the estimate.Fourmula0.7.2 (Large Sample) Testing the significance of the difference between the means of two samples.)To compare the means of two population we must understand the theory concerning the distribution of differences of sample means. Statisticians have determined that the distribution distribution difference between mean d (d Mean's) is approximately normal for large samples of n1 and n2. That is the distribution of differences of sample means is normal as long as neither n1 nor n2 Is less than 30. We can therefore use the probabilities associated with the normal distribution to construct confidence intervals and to perform hypothesis tests associated with this distribution.PROCUEDURS:-1. To compare the (μ1) mean of population 1 with the mean (μ2), of population 2 two independent random random samples of sizes n1 and n2 are to be selected from population 1 and population 2 respectively.By independent we mean that the sample drawn from population 1, in no way affects the sample drawn from population 2 fro example drawing two samples from men population and women population2. Compute (Mean1) and (Mean 2) i.e., mean of the sample 1 and 23. Computer the difference in the two samples means, d (mean) i.e,. d(Mean) = (Mean1 -Mean2).Thus for each pair of sample means of (Mean1) and (Mean2). a value of d(Mean) is obtained. The result is therefore a distribution of d(Mean)s.4. If μ1 and σ1 are the parameters of population 1. and μ2 and σ2 are the parameters of population 2, then for the distribution of d(Mean)s the menu μd(Mean)s is given by the equationμd(Mean)s = μ1 - μ2 the mean of the difference of the distribution of mean is the difference of the means of the two populations being compared.5. The standard deviation (or standard error) of the distribution of d(mean)s (written as σd(Mean)s) is given by the equation(Large Sample) Testing the significance of the difference between the means of two samples.)1. Point Estimation:- According to Central Limit Theorem for large samples the means of sampling distribution are normally distributed. The procedure that is frequently used to obtain a point estimate for the m of some population involves the following steps:(a) Select a representation (random) sample of the population.(b) Determine the mean (Mean) of the sample data(c) Assert that the value of M is the corresponding value of (Mean) i.e., = μ.2. Interval Estimation:-An extension of the above method of obtaining an estimate for μ is with the confidence interval, i.e., an interval estimate for μ.The advantages of interval estimate are:1. Interval estimate is more likely to be correct than the point estimate.2. We can calculate the probability that a given interval contains the mean of a population. We therefore speak of a specific interval as having "90' per cent probability of containing μ.3. We can choose the value of the probability we want for a given interval before we actually construct it.Recall that the central limit theorem asserts that for large sample sizes, the means are normally distributed. Furthermore, we know that any given mean (Mean) value can be standardized with the equation.Where μ = Mean of the populationμ.(Mean) = Mean of the sampling distribution of means.σ (Mean) = standard error or sampling distributionSinceμ.(Mean) μ we can write the following equationNow, with a given pair of Z values associated with some percentage of the Z distribution and equation, we can determine an upper and lower boundary for the same percentage of (Mean) values in the given mean distribution.
Compare the efficiency of simple random sampling with systematic random sampling for estimating the population mean and give your comments?
Compare the efficiency of simple random sampling with systematic random sampling for estimating the population mean and give your comments.
When is the sample mean over repeated samples from the same population or process not normally distributed?
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
Is it possible that population standard deviation is given but population mean is not given?
Yes.
Do small samples and large population variances usually underestimate or be close to population mean?
Small samples and large population variances imply that the estimate for the mean will be relatively poor. Whether or not it will result in an underestimate or overestimate depends on the distribution: with a symmetric distribution the two outcomes are equally likely.
Another term used to describe the average is called the?
The "average" of the population of samples is the same as their "mean".
What is the difference between population and sample distribution?
Sampling distribution is the probability distribution of a given sample statistic. For example, the sample mean. We could take many samples of size k and look at the mean of each of those. The means would form a distribution and that distribution has a mean, a variance and standard deviation. Now the population only has one mean, so we can't do this. Population distribution can refer to how some quality of the population is distributed among the population.
What is standard deviation of the mean?
If repeated samples are taken from a population, then they will not have the same mean each time. The mean itself will have some distribution. This will have the same mean as the population mean and the standard deviation of this statistic is the standard deviation of the mean.
What are the advantages and disadvantages of random sampling?
The main advantage is that the sample is representative of the population and the mean of the sample is an unbiased estimate of the population mean. Also, characteristics of other statistics based on the sample are well understood. However, sometimes it may not be possible to gather valid information from a sampling unit and then the sample is no longer random. This can be either because the sampling unit cannot be located or has been compromised by external factors. This can be particularly serious if the "missing" units share a common characteristic. Also, simple random samples may not include any units representing characteristics that are rare in the population - but important in the context of the experiment.
