Question: Consider the following questions about CI’s.

A researcher tests emotional intelligence (El) 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, \(\sigma \), 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.

For the values given above, the limits of the 95% CI are as follows:

Lower limit = 130 - 1.96 x 1.37 = 127.31;

Upper limit = 130 + 1.96 x 1.37 = 132.69.

The following exercises ask you to experiment to see how changing some of the values involved in computing the CI influences the width of the CI.

Recalculate the CI above to see how the lower and upper limits (and the width of the CO change as you vary the N in the sample (and leave all the other values the same).

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?
2. 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 but you change the value of N to 25?
3. 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 49?
4. 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?
5. 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)?
6. What are the upper and lower limits and the width of the CI if you change the confidence level to 99% (continue to use M = 130, s = 15, and N = 49)?
7. How does increasing the level of confidence from 80% to 99% affect the width of the CI?

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