Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Batteries of type $A$ have a mean life of $150$ hours. The task is to determine whether a fresh battery type, type $B$, has a smaller mean life than type $A$ batteries.
(a)[1]
State one reason for using a sample instead of the entire population when carrying out this test.
(b)[5]
A random sample of $120$ type $B$ batteries is tested and their mean life is found to be $147$ hours, while an unbiased estimate of the population variance is $225\,\text{hours}^2$. Test, at the $2\%$ significance level, whether type $B$ batteries have a shorter mean life than type $A$ batteries.
(c)[3]
Find a $94\%$ confidence interval for the population mean life of type $B$ batteries.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Any valid sampling reason, such as the population being too large, the cost being too high, or the test being destructive” …