11. Consider the following questions about CIs (Confidence intervals). 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 emotional intelligence EI for the entire school. The population standard deviation, , for EI is not known. Let’s suppose that a researcher wants to set up a 95% (Confidence intervals) 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 CI) change as you vary the N in the sample (and leave all the other values the same). a. What are the upper and lower limits of the CI and the width of the 95% CI 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 = __________ and upper limit = __________. Width (upper limit – lower limit)= ________________________. Note that when you change N, you need to change two things; the computed value of SEM and the degree of freedom used to look up the critical value for t. b. What are the upper and lower limits of the CI and the width of the 95% CI if all 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) = ________________________. c. 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 can change the value of N to 49? For N = 40, lower limit = __________ and upper limit = ______________. Width (upper limit – lower limit) = _______________________________. d. Based on the number you reported for sample size N of 16, 25, and 49, how does the width of the CI change as in (the number of cases in the sample) increases? e. What are the upper and lower limits and the width of the CI if you change the confidence level to 80% (and continue to use M = 130, s = 15, and N = 49)? For the 80% CI, lower limit = ___________ and upper limit = ____________. Width (upper limit - lower limit)= ____________________________. f. 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)? For a 99% CI, lower limit = __________ and upper limit = _____________. Width (upper limit - lower limit) = _____________________________. g. How does increasing the level of confidence from 80% to 99% affect the width of the CI? This question provided info in the begining and then ask for a-g to be answered. Thanks Lynda
11. Consider the following questions about CIs (Confidence intervals).
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 emotional intelligence EI for the entire school. The population standard deviation, , for EI is not known.
Let’s suppose that a researcher wants to set up a 95% (Confidence intervals) 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.
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 CI) change as you vary the N in the sample (and leave all the other values the same).
a. What are the upper and lower limits of the CI and the width of the 95% CI 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 = __________ and upper limit = __________. Width (upper limit – lower limit)= ________________________.
Note that when you change N, you need to change two things; the computed value of SEM and the degree of freedom used to look up the critical value for t.
b. What are the upper and lower limits of the CI and the width of the 95% CI if all 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) = ________________________.
c. 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 can change the value of N to 49?
For N = 40, lower limit = __________ and upper limit = ______________. Width (upper limit – lower limit) = _______________________________.
d. Based on the number you reported for sample size N of 16, 25, and 49, how does the width of the CI change as in (the number of cases in the sample) increases?
e. What are the upper and lower limits and the width of the CI if you change the confidence level to 80% (and continue to use M = 130, s = 15, and N = 49)?
For the 80% CI, lower limit = ___________ and upper limit = ____________.
Width (upper limit - lower limit)= ____________________________.
f. 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)?
For a 99% CI, lower limit = __________ and upper limit = _____________.
Width (upper limit - lower limit) = _____________________________.
g. How does increasing the level of confidence from 80% to 99% affect the width of the CI?
This question provided info in the begining and then ask for a-g to be answered. Thanks Lynda
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