A. Consider all samples of size 5 from this population:2, 5, 6, 8, 10, 12, 13 1. Compute the mean and the standard deviation of the population. 2. List all samples of size 5 and compute the mean for each sample. Samples Mean 3. Construct the sampling distribution of the sample means. Sampling Distribution of Sample Means Frequency Sample Mean Probability
A. Consider all samples of size 5 from this population:2, 5, 6, 8, 10, 12, 13 1. Compute the mean and the standard deviation of the population. 2. List all samples of size 5 and compute the mean for each sample. Samples Mean 3. Construct the sampling distribution of the sample means. Sampling Distribution of Sample Means Frequency Sample Mean Probability
A. Consider all samples of size 5 from this population:2, 5, 6, 8, 10, 12, 13 1. Compute the mean and the standard deviation of the population. 2. List all samples of size 5 and compute the mean for each sample. Samples Mean 3. Construct the sampling distribution of the sample means. Sampling Distribution of Sample Means Frequency Sample Mean Probability
Consider all samples of size 5 from this population:2, 5, 6, 8, 10, 12, 13
Compute the mean and the standard deviation of the population.
List all samples of size 5 and compute the mean for each sample.
Samples
Mean
Construct the sampling distribution of the sample means.
Sampling Distribution of Sample Means
Sample Mean
Frequency
Probability
Calculate the mean of the sampling distribution of the sample means. Compare this to the mean of the population.
Calculate the standard deviation of the sampling distribution of the sample means. Compare this to the standard deviation of the population.
Transcribed Image Text:A. Consider all samples of size 5 from this population:2, 5, 6, 8, 10, 12, 13
1. Compute the mean and the standard deviation of the population.
2. List all samples of size 5 and compute the mean for each sample.
Samples
Mean
3. Construct the sampling distribution of the sample means.
Sampling Distribution of Sample Means
Sample Mean
Frequency
Probability
4. Calculate the mean of the sampling distribution of the sample means. Compare this to the
mean of the population.
5. Calculate the standard deviation of the sampling distribution of the sample means. Compare
this to the standard deviation of the population.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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