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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.
When population distribution is right skewed is the sampling also with right skewed distribution?
If the population distribution is roughly normal, the sampling distribution should also show a roughly normal distribution regardless of whether it is a large or small sample size. If a population distribution shows skew (in this case skewed right), the Central Limit Theorem states that if the sample size is large enough, the sampling distribution should show little skew and should be roughly normal. However, if the sampling distribution is too small, the sampling distribution will likely also show skew and will not be normal. Although it is difficult to say for sure "how big must a sample size be to eliminate any population skew", the 15/40 rule gives a good idea of whether a sample size is big enough. If the population is skewed and you have fewer that 15 samples, you will likely also have a skewed sampling distribution. If the population is skewed and you have more that 40 samples, your sampling distribution will likely be roughly normal.
Describe the central limit theorem and give an example of how it can be used in statistics?
The Central Limit Theorem (CLT) is a theorem that describes the fact that if a number of samples are taken from a population, the distribution of the means of the samples will be normal. This is true for all different distributions, whether or not the population is normal or something else. The main exception to this is that the theorem does not work particularly well if the samples are small (
The X2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5000 observations and is divided into 6 categories?
It can be.
What sample size is needed to disprove the hypothesis that the probability of outcome A equals 0.25?
The answer depends on what population characteristic A measures: whether it is mean, variance, standard deviation, proportion etc. It also depends on the sampling distribution of A.
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.
What distribution does the F distribution approach as the sample size increases?
The F distribution is used to test whether two population variances are the same. The sampled populations must follow the normal distribution. Therefore, as the sample size increases, the F distribution approaches the normal distribution.
What is a difference between F statistics F distribution?
An F-statistic is a measure that is calculated from a sample. It is a ratio of two lots of sums of squares of Normal variates. The sampling distribution of this ratio follows the F distribution. The F-statistic is used to test whether the variances of two samples, or a sample and population, are the same. It is also used in the analysis of variance (ANOVA) to determine what proportion of the variance can be "explained" by regression.
When population distribution is right skewed is the sampling also with right skewed distribution?
If the population distribution is roughly normal, the sampling distribution should also show a roughly normal distribution regardless of whether it is a large or small sample size. If a population distribution shows skew (in this case skewed right), the Central Limit Theorem states that if the sample size is large enough, the sampling distribution should show little skew and should be roughly normal. However, if the sampling distribution is too small, the sampling distribution will likely also show skew and will not be normal. Although it is difficult to say for sure "how big must a sample size be to eliminate any population skew", the 15/40 rule gives a good idea of whether a sample size is big enough. If the population is skewed and you have fewer that 15 samples, you will likely also have a skewed sampling distribution. If the population is skewed and you have more that 40 samples, your sampling distribution will likely be roughly normal.
Answers to smu assisgnment 1st semester?
1. The percentage sugar content of Tobacco in two samples was represented in table 11.11. Test whether their population variances are same. [ 10 marks]Table 1. Percentage sugar content of Tobacco in two samplesSample A2.42.72.62.12.5Sample B2.73.02.83.12.23.6
How do you compare distrubutions?
The answer depends on whether you are comparing the means or variances of similar distributions or whether you are comparing the distributions themselves. There are many statistical tests for comparing distributions: the best test depends on whether or not the distribution is known in terms of its parameters, or in less specific terms.
When to use t-test?
You use the t-test when the population standard deviation is not known and estimated by the sample standard deviation. (1) To test hypothesis about the population mean (2) To test whether the means of two independent samples are different. (3) To test whether the means of two dependent samples are different. (4) To construct a confidence interval for the population mean.
Describe the central limit theorem and give an example of how it can be used in statistics?
The Central Limit Theorem (CLT) is a theorem that describes the fact that if a number of samples are taken from a population, the distribution of the means of the samples will be normal. This is true for all different distributions, whether or not the population is normal or something else. The main exception to this is that the theorem does not work particularly well if the samples are small (
What is the different between population density and population distribution?
The way in which people are spread across a given area is known as population distribution. Geographers study population distribution patterns at different scales: local, regional, national, and global. Patterns of population distribution tend to be uneven. For example, in Ireland there are more people living in the south and east than in the border counties and the west. Population density is the average number of people per square kilometre. It is a way of measuring population distribution. It shows whether an area is sparsely or densely populated. Population density is calculated using the following formula: Population density = total population divided by total land area in km²
How do you find the population mean for a 95 percent confidence interval?
It depends whether or not the observations are independent and on the distribution of the variable that is being measured or the sample size. You cannot simply assume that the observations are independent and that the distribution is Gaussian (Normal).
The X2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5000 observations and is divided into 6 categories?
It can be.
What is the purpose of the Levene's test?
Levene's test is used to assess whether the variances of two or more groups are equal. It is commonly employed in statistical analysis to determine if the assumption of homogeneity of variances is met, which is important for certain statistical tests such as the t-test and ANOVA.
