A roadside study found that 62% of petrol cars in its sample had CO2 _2\,2 emissions above 150 g/km. The study sampled cars from three regions during one year.
Sam takes a random sample of 28 petrol cars from a garage and wishes to test, at the 10% significance level with a probability of at most 0.05 in each tail, whether the proportion of petrol cars with CO2 _2\,2 emissions above 150 g/km differs from 62%.
Find the critical region for Sam's test.
Find the actual significance level of a test based on this critical region.
In Sam's sample, 23 of the cars have CO2 _2\,2 emissions above 150 g/km. State Sam's conclusion in context.
Using the information about the original study, give one reason why Sam's conclusion cannot be applied to all petrol cars registered in England.