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 = 123.808 and upper limit = 132.196   width (upper limit-lower limit) = 132.196 -123,808 = 12.384
• 
  
• 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 = 125.6907, and upper limit = 134.3093, width (upper limit – lower limit) = 134.3093 -125.6907 = 8.6186
• 
  
• Based on the numbers you reported for sample sizes 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) =