Infer a normal population mean and conduct a one-tailed 5% hypothesis test.

An urban highway has a speed limit of \(50\text{ km h}^{-1}\). Vehicle speeds are normally distributed with a standard deviation of \(10\text{ km h}^{-1}\), and 30% of vehicles exceed the speed limit.

1. Show that the mean speed of the vehicles is approximately \(44.8\text{ km h}^{-1}\). The police conduct a “Safer Driving” campaign intended to encourage slower driving and want to know whether it has been effective. A sample of 25 vehicles has a mean speed of \(41.3\text{ km h}^{-1}\).[3]
2. Given that the null hypothesis is \(H_0\): the mean speed has been unaffected by the campaign, state \(H_1\), the alternative hypothesis.[1]
3. State whether a one-tailed or two-tailed test is appropriate for these hypotheses, and explain why.[2]
4. Has the campaign had significant effect at the 5% level?[4]