researcher tests emotional intelligence (EI) for a random sample of children selected from a population of all students who are enrolled in a school for gifted children. The researcher wants to estimate the mean EI for the entire school. The population standard deviation, mean, for EI is not known. Let’s suppose that a researcher wants to set up a 95% CI for IQ scores using the following information: The sample mean M= 130 The sample standard deviation s = 15. The sample size N = 120. The df = N – 1 = 119 What are the upper and lower limits of the CI and the width of the 95% CI if all the other values remain the same (M = 130, s =15) but you change the value of N to 16? For N = 16, lower limit = 122.41 and upper limit=137.58 width (upper limit-lower limit = 15,17 What are the upper and lowers of CI and the width of 95% CI if all the other values remain the same but you change the value of N to 25? . For N = 25, lower limit = and upper limit = width (upper limit-lower limit) = What are the upper and lower limits of CI and the width of the 95% CI if all the other values remain the same (M = 130, s = 15) but you change the value of N to 49? For N = 49, lower limit = and upper limit = . width (upper limit – lower limit) = Based on the numbers you reported for sample size N of 16, 25, and 49, how does the width of the CI change as N (the number of cases in the sample) increases? What are the upper and lower limits and the width of this Ci if you change the confidence level to 80% (and continue to use M = 130, s = 15, and N = 49)? For an 80% CI, lower limit = and upper limit = width (upper limit – lower limit) = What are the upper and lower limits and width of the CI if you change the confidence level to 99% (continue to use M= 130, s =15, and N =49)? For a 99% CI, lower limit = and upper limit = width (upper limit – lower limit) = How does increasing the level of confidence from 80% to 99% affect the width of the CI?

Solution : Given information: M= 130 Sample mean s= 15 sample standard deviations n= 150 sample…

Answered: researcher tests emotional intelligence (EI) for a random sample of children selected from a population of all students who are enrolled in a school for gifted…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

Consider the following questions about CIs.

A researcher tests emotional intelligence (EI) for a random sample of children selected from a population of all students who are enrolled in a school for gifted children. The researcher wants to estimate the mean EI for the entire school. The population standard deviation, mean, for EI is not known. Let’s suppose that a researcher wants to set up a 95% CI for IQ scores using the following information:

The sample mean M= 130

The sample standard deviation s = 15.

The sample size N = 120.

The df = N – 1 = 119

What are the upper and lower limits of the CI and the width of the 95% CI if all the other values remain the same (M = 130, s =15) but you change the value of N to 16?

For N = 16, lower limit = 122.41 and upper limit=137.58 width (upper limit-lower limit = 15,17

What are the upper and lowers of CI and the width of 95% CI if all the other values remain the same but you change the value of N to 25? . For N = 25, lower limit = and upper limit = width (upper limit-lower limit) =
What are the upper and lower limits of CI and the width of the 95% CI if all the other values remain the same (M = 130, s = 15) but you change the value of N to 49? For N = 49, lower limit = and upper limit = . width (upper limit – lower limit) =
Based on the numbers you reported for sample size N of 16, 25, and 49, how does the width of the CI change as N (the number of cases in the sample) increases?
What are the upper and lower limits and the width of this Ci if you change the confidence level to 80% (and continue to use M = 130, s = 15, and N = 49)? For an 80% CI, lower limit = and upper limit = width (upper limit – lower limit) =
What are the upper and lower limits and width of the CI if you change the confidence level to 99% (continue to use M= 130, s =15, and N =49)? For a 99% CI, lower limit = and upper limit = width (upper limit – lower limit) =
How does increasing the level of confidence from 80% to 99% affect the width of the CI?

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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