8.1 Sampling Distributions
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A) According to the central limit theorem, the sampling distribution of x becomes approximately normal as the sample size n increases, regardless of the shape of the population. This means that the shape of the sampling distribution of x is approximately normal. B) U=U-x, value is always same To get o-x, divide o by square root of sample size n C) Simple input in calculator, ensuring lower and upper values are satisfied properly. Also, make sure to not use the original "o" value, but the one from dividing by the square root of the sample size.
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A) Center of distribution of the sample means is found by selecting the middle value of the distribution chart. B) We are going to subtract the far right value from the center value
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C) Notice that in this case the distribution of the sample mean is normal and the sample size is small. The sampling distribution of the mean is only normal when the population is normal or the sample size is large. D) Read and see formula.
True or False To cut the standard error of the mean in half, the sample size must be doubled.
False. The sample size must be increased by a factor of four to cut the standard error in half.
Sampling distribution of sample means
If the sample statistic is the sample mean
Sampling distribution
Is the probability of a sample statistic that is formed when samples of size n are repeatedly taken from a population.
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Sample means
Suppose that the mean time for an oil change at a 10-minute oil change joint is 11.4 minutes with a standard deviation of 3.2 minutes. A) If a random sample of n=35 oil changes is selected, describe the sampling distribution of the sample mean. B) If a random sample of n=35 oil changes is selected, what is the probability the mean oil change time is less than 11 minutes.
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Simply divide standard deviation by the sample size of the population. Simple. Notice that the first answer is already given to us.
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The sample mean matches the population mean, but the standard error of the mean depends on the sample size. Notice that as n increases, o-x decreases.
The Central Limit Theorem
The shape of the distribution of the sample mean becomes approximately normal as the sample size n increases, regardless of the shape of the population.
The standard deviation of the sampling distribution of x, denoted o-x is called
The standard error of the mean
True or False The distribution of the sample mean, x, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size
True.
