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What is the sampling distribution when the standard deviation is known?
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
What will the sampling distribution of the mean be if a population is normally distribution?
Also normally distributed.
In the population SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100?
The answer depends on what SAT tests. In the UK the mean is 100 and the SD approx 15 - the scores are truncated at 100 +/- 44.
When the population standard deviation is known the sample distribution is a?
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
When is a t-test performed instead of a z-test?
A t-test is performed instead of a z-test when the sample size is small (typically n < 30) and the population standard deviation is unknown. The t-test accounts for the increased variability and uncertainty in small samples by using the sample standard deviation rather than the population standard deviation. Additionally, it is often used when the data is approximately normally distributed.
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 If a certain statistician has an IQ of 140 what percent of the population has an IQ less than she does?
99.6% for
What percentage of the normally distributed population lies within the plus or minus one standard deviation of the population mean?
68.2%
When the population is normally distributed population standard deviation s is unknown and the sample size is n equals 15 the confidence interval for the population mean s is based on the?
The Z test.
What are the best statistics to use for data that is normally distributed?
The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.
True or false a distribution of sample means is normally distributed with a mean equal to the population mean and standard deviation equal to the standard error of the mean?
True.
Does a population have to be normally distributed in order to use the chi-square distribution?
No, but the approximation is better for normally distributed variables.
What is the sampling distribution when the standard deviation is known?
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
What will the sampling distribution of the mean be if a population is normally distribution?
Also normally distributed.
A particular fruit's weights are normally distributed, with a mean of 298 grams and a standard deviation of 13 grams.If you pick one fruit at random, what is the probability that it will weigh between 262 grams and 269 grams?
A particular fruit's weights are normally distributed, with a mean of 760 grams and a standard deviation of 15 grams. If you pick one fruit at random, what is the probability that it will weigh between 722 grams and 746 grams-----A particular fruit's weights are normally distributed, with a mean of 567 grams and a standard deviation of 25 grams.
In the population SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100?
The answer depends on what SAT tests. In the UK the mean is 100 and the SD approx 15 - the scores are truncated at 100 +/- 44.
When the population standard deviation is known the sample distribution is a?
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
Lets assume you have taken 100 samples of size 36 each from a normally distributed population Calculate the standard deviation of the sample means if the populations variance is 25?
square (25/36) = 5/6 = .833
