Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A researcher is checking whether the proportion of families in his town who do not own a car is different from the proportion for the country as a whole, which is 10.1%. He selects a large random sample of families from his town and records the proportion who do not own a car.
(a)[1]
Explain why a two-tailed test fits this context.
(b)[1]
State appropriate null and alternative hypotheses for the test.
(c)[2]
The researcher finds the test statistic $z$ and obtains $z = 1.82$. He performs the test at the 5% significance level. State the conclusion of the test, explaining your answer.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The researcher is seeking evidence of 'different from', not specifically 'less than' or 'more than'” …