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?

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Author:Amos Gilat
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 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

  1. 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

  1. 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) =
  2. 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) =
  3. 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?
  4. 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) =
  5. 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) =
  6. How does increasing the level of confidence from 80% to 99% affect the width of the CI?

 

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