00:01
In this problem, we are told that 20 % of the motorists regularly exceed the speed limit on a motorway.
00:06
A new law imposes penalties for speeding and since there has been a reduction in the number of motorists speeding.
00:15
We are told that a random sample of 30 motorists is taken, that means n is equal to 30.
00:21
And for part a of the problem, we have to write the null hypothesis that should be used to test the police's suspicion.
00:28
So the null hypothesis is given by capital p equal to 0 .20.
00:35
This means 20 % of the motorists regularly exceed the speed limit on a motorway and the alternative hypothesis is given by p is less than 0 .20.
00:47
This means that the population proportion of motorists exceeding the speed limit is less than 20%.
00:53
Next we have to find the critical region for a test.
00:56
It is given by z equal to p hat that is a sample proportion minus capital p divided by under root of capital p multiplied by one minus capital p divided by n sample proportion p not p hat is given by x divided by n that is three divided by 30 which is equal to 0 .1 now putting in the values we write 0 .1 minus 0 .20 divided by under root 0 .20 multiplied by 1 minus 0 .20 divided by 30...