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Your question is a bit difficult to understand. I will rephrase: In hypothesis testing, when the sample mean is close to the assumed mean of the population (null hypotheses), what does that tell you? Answer: For a given sample size n and an alpha value, the closer the calculated mean is to the assumed mean of the population, the higher chance that null hypothesis will not be rejected in favor of the alternative hypothesis.
What else can I help you with?
What happens to the sample mean as the sample size increases?
With a good sample, the sample mean gets closer to the population mean.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
What is population mean in statistics?
The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.
Why is the sample mean an unbiased estimator of the population mean?
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
What does it mean for a sample to representative of a population?
That the key characteristics of the population are reflected in the sample.
What happens to the sample mean as the sample size increases?
With a good sample, the sample mean gets closer to the population mean.
Is the sampling of error larger when the sample mean is closer to the population mean?
No.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Is the sample mean a consistent estimator of population mean?
Yes, the sample mean is a consistent estimator of the population mean. As the sample size increases, the sample mean converges in probability to the true population mean, provided that the samples are drawn independently and identically distributed from the population. This property is a result of the Law of Large Numbers, which states that larger samples will yield estimates that are closer to the actual population parameter.
What is population mean in statistics?
The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.
Are the sample mean and sample proportion of a population are called population parameters?
No, the sample mean and sample proportion are not called population parameters; they are referred to as sample statistics. Population parameters are fixed values that describe a characteristic of the entire population, such as the population mean or population proportion. Sample statistics are estimates derived from a sample and are used to infer about the corresponding population parameters.
Why is the sample mean an unbiased estimator of the population mean?
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
Difference between calculating the sample mean and the population mean?
The same basic formula is used to calculate the sample or population mean. The sample mean is x bar and the population mean is mu. Add all the values in the sample or population and divide by the number of data values.
The law of large numbers?
The law of large numbers states that as the number of observations in a sample increases, the sample mean will tend to approach the population mean. In other words, the larger the sample size, the more accurate the estimate of the population parameter. This law forms the basis for statistical inference and hypothesis testing.
What is the best estimator of population mean?
The best point estimator of the population mean would be the sample mean.
What is the difference between calculating the sample mean and the population mean?
You calculate the actual sample mean, and from that number, you then estimate the probable mean (or the range) of the population from which that sample was drawn.
Is N the sample or population mean?
N is neither the sample or population mean. The letter N represents the population size while the small case letter n represents sample size. The symbol of sample mean is x̄ ,while the symbol for population mean is µ.
