Question

1. A researcher wants to study whether students who live in dormitories are significantly more involved in campus life than students who commute to campus? A sample of 171 students who live in dormitories spend on average 10.5 hours per week to extracurricular activities with standard deviation of 1.9 hours. A sample of 161 students who commute to campus spend on average 12.4 hours per week to extracurricular activities with a standard deviation of 2.4.  At 90% level, is the difference between these randomly selected samples of commuter and residential students significant? Follow the five steps hypothesis testing and write your conclusion.

Answer 1

n1 = 171, n2 = 162, x1-bar = 10.5, x2-bar = 12.4, s1 = 1.9, s2 = 2.4

Ho: μ1 = μ2        

Ha: μ1 ≠ μ2        

α = 0.10       

Df = 171 + 161 - 2 = 330      

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)]

=   √(((171 - 1) * 1.9^2 + (161 - 1) * 2.4^2)/(171 + 161 -2))

= 2.157

SE = s * √{(1 /n1) + (1 /n2)}

= 2.157 * √((1/171) + (1/161))

= 0.2368      

t = (x1-bar -x2-bar)/SE = -8.022      

p- value =  0

Since the p- value < 0.10, there is a significant difference between the two groups on time spent towards campus life