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?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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
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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