Sampling behavior of a mean. Suppose you could take all possible samples of size n = 25 from a Normal population with mean μ = 50 and σ = 5. Question 10. Sketch or describe in words the sampling distribution of . Identify landmarks on the horizontal axis of this sampling distribution that are ±1 and ±2 standard deviations around its center.The sampling distribution of is N(50, 1); the marks ±1 standard deviations around its center are 49 and 51, and the marks ±2 standard deviations around its center are 48 and 52.The sampling distribution of is N(50, 5); the marks ±1 standard deviations around its center are 45 and 55, and the marks ±2 standard deviations around its center are 40 and 60.The sampling distribution of is N(50, 25); the marks ±1 standard deviations around its center are 25 and 50, and the marks ±2 standard deviations around its center are 0 and 100. Question 11. Would you be surprised to find a sample mean of 47 under these conditions? Explain your reasoning.Yes, it is less than 2 standard deviations from the center of its sampling distributionYes, it is greater than 2 standard deviations from the center of its sampling distributionNo, it is within 2 standard deviations from the center of its sampling distributionCannot be determined based on this information Question 12. Would you be surprised to find a sample mean of 51.5? Explain your reasoning. Yes, it is less than 2 standard deviations from the center of its sampling distributionYes, it is greater than 2 standard deviations from the center of its sampling distributionNo, it is within 2 standard deviations from the center of its sampling distributionCannot be determined based on this information Pediatric asthma survey, n = 250. Suppose that asthma affects 1 in 20 children in a population, and let’s assume we have collected a sample of 250 children from this population. Question 13. Can we use the Normal approximation to the binomial in this instance?YesNo Question 14. What is the probability of seeing at least 25 cases in a sample (use Normal approximation to the binomial)?< 0.0010.150.85> 0.999

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Sampling behavior of a mean. Suppose you could take all possible samples of size n = 25 from a Normal population with mean μ = 50 and σ = 5.

Question 10. Sketch or describe in words the sampling distribution of . Identify landmarks on the horizontal axis of this sampling distribution that are ±1 and ±2 standard deviations around its center.

The sampling distribution of is N(50, 1); the marks ±1 standard deviations around its center are 49 and 51, and the marks ±2 standard deviations around its center are 48 and 52.
The sampling distribution of is N(50, 5); the marks ±1 standard deviations around its center are 45 and 55, and the marks ±2 standard deviations around its center are 40 and 60.
The sampling distribution of is N(50, 25); the marks ±1 standard deviations around its center are 25 and 50, and the marks ±2 standard deviations around its center are 0 and 100.

Question 11. Would you be surprised to find a sample mean of 47 under these conditions? Explain your reasoning.

Yes, it is less than 2 standard deviations from the center of its sampling distribution
Yes, it is greater than 2 standard deviations from the center of its sampling distribution
No, it is within 2 standard deviations from the center of its sampling distribution
Cannot be determined based on this information

Question 12. Would you be surprised to find a sample mean of 51.5? Explain your reasoning.

Yes, it is less than 2 standard deviations from the center of its sampling distribution
Yes, it is greater than 2 standard deviations from the center of its sampling distribution
No, it is within 2 standard deviations from the center of its sampling distribution
Cannot be determined based on this information

Pediatric asthma survey, n = 250. Suppose that asthma affects 1 in 20 children in a population, and let’s assume we have collected a sample of 250 children from this population.

Question 13. Can we use the Normal approximation to the binomial in this instance?

Question 14. What is the probability of seeing at least 25 cases in a sample (use Normal approximation to the binomial)?

< 0.001
0.15
0.85
> 0.999

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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