Question

Activity Two: Hypothesis Testing of Two Means Suppose that in the same context as the previous activity, some of the people completing the pen and paper form also complete the online form. The difference in time between the two tasks is calculated for 101 such individuals, and reported as di = online timei – offline timei. Suppose the sample mean and standard deviation of the variable di is reported to be 30 seconds and 1.3 minutes respectively. Is there a significant difference in the time taken for each task at the 95% level? Pretend that you have no a priori convictions about which is quicker (i.e., two tailed test).

Answer 1

Ho :µd=0

Ha :µd ╪0

Level of Significance , α = 0.05

sample size , n = 101

mean of difference , D̅ =30.0000

std dev of difference , Sd = 1.3000

std error , SE = Sd / √n = 0.1294

t-statistic   = (D̅ - µd)/SE   = 231.9202

Degree of freedom,    DF=n - 1 = 100

p-value = 0.0000

Conclusion:                            p-value <α , Reject null hypothesis

so, there is a significant difference in the time taken for each task at the 95% level