Novice: What is the 95 % confidence interval of the mean of a sample of 100 spot speed observations with empirical mean 55 km/h and 8 km/h of standard deviation (given that for a variable X following the normal distribution, P(X<=1.96)=0.975 and P(X<=1.64)=0.95)?

• [53.43, 56.57]
• [47.00, 61.00]
• [53.69, 56.31]
• [54.20, 55.80]

Expert: Speeds were measured before and after a traffic calming operation in a residential neighbourhood. The null hypothesis H0 is that mean speed did not change and the alternative hypothesis is that it decreased. The empirical means and standard deviations are computed from large samples of observations before and after. Given that the test statistic is 1.23 and that for a variable X following the normal distribution, P(X<=1.28)=0.90 and P(X<=1.64)=0.95, conclude whether the traffic calming had a significant effect on traffic speed.

• 1.23 is smaller than 1.64 and therefore the null hypothesis can be rejected at the 95 % confidence level.
• 1.23 is smaller than 1.28 and therefore the null hypothesis cannot be rejected at the 90 % confidence level.
• One cannot answer since the test statistic follows the Student distribution.
• One needs to first test if both speed distributions follow the normal distribution.