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When the sample size is large valid confidence intervals can be established for the population mean irrespective of the shape of the underlying distribution?
Yes, but that begs the question: how large should the sample size be?
What is The mean of a discrete probability distribution is also called the?
The mean of a discrete probability distribution is also called the Expected Value.
A sample of 24 observations is taken from a population that has 150 elements The sampling distribution of the mean is?
A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is
The mean or expected value of the distribution of a discrete random variable is?
30.47
What does a negative kurtosis mean?
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
What is the shape of the distribution of the mean of a sample?
The mean of a sample is a single value and so its distribution is a single value with probability 1.
Which of the following is true regarding the sampling distribution of the mean for a large sample size?
It has the same shape, mean, and standard deviation as the population.
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
Assume that you have a binomial experiment with p 0.5 and a sample size of 100. The expected value of this distribution is?
In a binomial distribution, the expected value (mean) is calculated using the formula ( E(X) = n \times p ), where ( n ) is the sample size and ( p ) is the probability of success. For your experiment, with ( n = 100 ) and ( p = 0.5 ), the expected value is ( E(X) = 100 \times 0.5 = 50 ). Thus, the expected value of this binomial distribution is 50.
How much error is expected between the sample mean and population mean?
0. The expected value of the sample mean is the population mean, so the expected value of the difference is 0.
When the sample size is large valid confidence intervals can be established for the population mean irrespective of the shape of the underlying distribution?
Yes, but that begs the question: how large should the sample size be?
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.
How do you calculate distribution of sample means?
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.
What is the mean of the sampling distribution of the sample mean?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
What is the mean of the sample means that is normally distributed with a mean of 10 standard deviation of 2 and a sample size f 25?
The mean of the sample means, also known as the expected value of the sampling distribution of the sample mean, is equal to the population mean. In this case, since the population mean is 10, the mean of the sample means is also 10. The standard deviation of the sample means, or the standard error, would be the population standard deviation divided by the square root of the sample size, which is ( \frac{2}{\sqrt{25}} = 0.4 ).
How do you determine your sample score on the comparison distribution?
To determine your sample score on the comparison distribution, you first need to calculate the sample mean and standard deviation. Then, you can use these statistics to find the z-score, which indicates how many standard deviations your sample mean is from the population mean. By comparing this z-score to critical values from the standard normal distribution, you can assess the significance of your sample score in relation to the comparison distribution.
What is the mean of a normal distribution?
It is the expected value of the distribution. It also happens to be the mode and median.It is the expected value of the distribution. It also happens to be the mode and median.It is the expected value of the distribution. It also happens to be the mode and median.It is the expected value of the distribution. It also happens to be the mode and median.
