3. A researcher randomly selects a sample of 61 former student leaders from a list of graduates of UNCG who had participated in leadership positions while a student. She discovered that it has taken an average of 4.97 years for these student leader graduates to finish their degrees, with a standard deviation of 1.23. The average for the entire student body is 4.56 years. Is the difference between student leaders and the entire student population statistically significant at the alpha

not statistically significant at ∝ = 0.05

Step-by-step explanation:

Sample size( n )  = 61

Average for student leader graduates to finish degree ( x') = 4.97 years

std = 1.23

Average for student body = 4.56 years

Determine if the difference between the student leaders and the entire student population is statistically significant at alpha

H0( null hypothesis ) : u = 4.56

Ha : u ≠ 4.56

using test statistic

test statistic ; t = ( x' - u ) / std√ n

                        = ( 4.97 - 4.56 ) / 1.23 √ 61

                        = 2.60

let ∝ = 0.05 , critical value = -2.60 + 2.60

Hence we wont fail to accept  H0

This shows that the difference between the student leaders and the entire student population is not statistically significant at ∝ = 0.05