Hypothesis tests for a meanEdexcel International A Level Further Maths: Flashcards

What these 14 flashcards ask

What is the null hypothesis for a test of a mean?
When is a test one-tailed rather than two-tailed?
Test statistic for a mean with \sigma known?
Critical values for one-tailed 5\% and 1\% tests?
Critical values for two-tailed 5\% and 1\% tests?
What is a significance level?
What is a p-value?
How do you use a p-value in a two-tailed test?
What is a critical region?
State the Central Limit Theorem for \bar X.
When is the Central Limit Theorem used in a test?
What do you do if \sigma^2 is unknown and n is large?
How should a conclusion be worded?
Can hypotheses be written in terms of \bar x?

Exam questions on Hypothesis tests for a mean

A manufacturer claims that the lifetimes of its light bulbs are Normally distributed with mean $1200$ hours and standard deviation $80$ hours. A consumer group believes that the mean lifetime is lower than claimed. A random sample of $16$ bulbs has a mean lifetime of $1165$ hours. Assume that the standard deviation is $80$ hours.
Carry out the test at the $5\%$ significance level and state your conclusion in context.2 marks
A machine fills cartons with orange juice. The volume is Normally distributed with standard deviation $6$ ml, and the mean volume is meant to be $500$ ml. A quality manager takes a random sample of $25$ cartons, which has a mean volume of $502.7$ ml, and tests at the $5\%$ significance level whether the mean volume has changed.
Complete the test and state your conclusion in context.2 marks
The time, in minutes, that a customer waits to be served at a call centre has an unknown, positively skewed distribution with standard deviation $3.5$ minutes. The centre claims that the mean waiting time is $5.8$ minutes, but a consumer group believes it is longer. A random sample of $49$ customers has a mean waiting time of $6.4$ minutes.
Explain why the sample mean can be assumed to be approximately Normally distributed, and state its approximate distribution if the centre's claim is correct.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).