Hypothesis tests for a Normal meanEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

If X\sim N(\mu,\sigma^2), what is the distribution of the sample mean \bar X for a sample of size n?
What is the standard error?
What happens to the standard error as n increases?
In terms of what are the hypotheses written?
What is the test statistic for a Normal mean?
Critical z for a 5% two-tailed test?
Critical z for a 5% one-tailed test?
Critical z for a 1% lower-tail test?
What do you compare with in a two-tailed test at 5% using a p-value?
What must be known or assumed for this test?
\sigma=4, n=25: find the standard error.
How do you find the critical values of \bar x for a two-tailed test?
What conclusion follows when H0 is not rejected?

Exam questions on Hypothesis tests for a Normal mean

The masses of packets of cereal, in grams, are Normally distributed with standard deviation 4. The packets are labelled with a mean mass of 500 g. A consumer group suspects that the true mean mass $\mu$ is less than 500 g. It tests this at the 1% significance level using a random sample of 25 packets, with sample mean $\bar X$ .
Given that $P(Z<-2.5)=0.0062$ , state the conclusion of the test, in context.2 marks
The time $T$ minutes taken by workers to assemble a component is Normally distributed with standard deviation 1.5. A supervisor claims that the mean time $\mu$ is 12 minutes. A researcher believes that the mean time is different, and tests this at the 5% significance level using a random sample of 36 workers, with sample mean $\bar T$ .
Find the critical values for $\bar T$ for this test.2 marks
The lengths of rods made by a machine, in millimetres, are Normally distributed with standard deviation 0.8. The machine is set to produce rods with mean length 50. After maintenance the manager believes that the mean length $\mu$ has increased. A random sample of 16 rods has mean length 50.45 mm.
State the hypotheses for a test at the 5% significance level, and the distribution of the sample mean $\bar X$ if the null hypothesis is true.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).