Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A firm manufactures a particular kind of battery-powered toy. Let the battery life be denoted by $X$ hours, and suppose the population mean of $X$ is claimed to be $12$. The Quality Control department wanted to investigate whether the true population mean of $X$ is actually below $12$. They took a random sample of $50$ of these toys and obtained the sample mean $\bar{X}=11.4$.
(a)[1]
State appropriate null and alternative hypotheses for the test.
(b)[2]
You may take the standard deviation of the battery life to be $2.3$ hours. Show that the value $\bar{X} = 11.4$ causes the null hypothesis to be rejected at the $5\%$ significance level.
(c)[2]
You are told that the value $\bar{X} = 11.4$ causes the null hypothesis to be rejected at the $\alpha\%$ significance level. Find the set of possible values of $\alpha$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct pair of hypotheses $H_0:\mu=12$, $H_1:\mu<12$” …