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Is it necessary that sample sizes be equal for a two sample test?
No.
How large should a sample size be?
The ideal sample size depends on several factors, including the population size, the desired confidence level, the margin of error, and the variability within the population. Generally, larger sample sizes yield more reliable results and reduce the margin of error. For most surveys, a sample size of 30 is often considered the minimum for general statistical analysis, but larger sizes (e.g., 100-400) are recommended for more accurate and generalizable findings. It's essential to conduct a power analysis to determine the specific sample size needed for your study's objectives.
Does the central limit theorem allows the use of the normal distribution to analyze the sample mean if the sample sizes are large enough?
Yes. Roughly, very large samples are very likely to have subsets data points having very similar means and distributions. Large numbers of such subsets will tend to be normal distributed (Why?) and will tend to make the total sample be normally distributed.
Which estimator will consistently have an approximately normal distribution?
The sample mean is an estimator that will consistently have an approximately normal distribution, particularly due to the Central Limit Theorem. As the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the original population's distribution, provided the samples are independent and identically distributed. This characteristic makes the sample mean a robust estimator for large sample sizes.
What are the advantages and disadvantages of chi-square?
The chi-square test is advantageous because it is simple to use, does not require assumptions about the distribution of the data, and can handle large sample sizes effectively. It is particularly useful for categorical data analysis, helping to determine if there is a significant association between variables. However, its disadvantages include sensitivity to sample size, as large samples can lead to statistically significant results even for trivial associations, and it is not suitable for small sample sizes or when expected frequencies are low. Additionally, chi-square tests do not provide information about the strength or direction of the relationship.
Disadvantages of a large sample size confidence Interval in statistices?
A disadvantage to a large sample size can skew the numbers. It is better to have sample sizes that are appropriate based on the data.
When designing an experiment a benefit of larger sample sizes would be more?
Accurate estimates of various statistics.
Does the Student t distribution takes different values for a different sample size?
Yes, but it converges to the Gaussian (Normal) dirstribution for large sample sizes.
Is it necessary that sample sizes be equal for a two sample test?
No.
How large should a sample size be?
The ideal sample size depends on several factors, including the population size, the desired confidence level, the margin of error, and the variability within the population. Generally, larger sample sizes yield more reliable results and reduce the margin of error. For most surveys, a sample size of 30 is often considered the minimum for general statistical analysis, but larger sizes (e.g., 100-400) are recommended for more accurate and generalizable findings. It's essential to conduct a power analysis to determine the specific sample size needed for your study's objectives.
Does the central limit theorem allows the use of the normal distribution to analyze the sample mean if the sample sizes are large enough?
Yes. Roughly, very large samples are very likely to have subsets data points having very similar means and distributions. Large numbers of such subsets will tend to be normal distributed (Why?) and will tend to make the total sample be normally distributed.
What size are the sample sizes at fashion shows?
Sample sizes vary from designer to designer but a common range is between 0-2, 4 at most.
What is the function of allele ladder in DNA profiling?
An allele ladder is used as a reference for determining the sizes of DNA fragments in a sample during DNA profiling. It contains known fragments of DNA of varying sizes that are used to calibrate the gel electrophoresis results, allowing for accurate comparison and identification of the sizes of DNA fragments in the sample.
What does the Central Limit Theorem say about the traditional sample size that separates a large sample size from a small sample size?
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
Which is the correct set of assumptions needed for comparing 3 or more means?
Equal variances, independent observations and normality
Which estimator will consistently have an approximately normal distribution?
The sample mean is an estimator that will consistently have an approximately normal distribution, particularly due to the Central Limit Theorem. As the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the original population's distribution, provided the samples are independent and identically distributed. This characteristic makes the sample mean a robust estimator for large sample sizes.
In a controlled experiment how do the number of trials and sample sizes effect the results?
The number of trials and sample sizes generally increase the accuracy of the results because you can take the average or most common results in the experiment
