A safety engineer tests the breaking strength of steel cables. The manufacturer claims the cables have a mean breaking strength of 80 kN. The engineer suspects the cables are weaker than claimed. Data from 200 cables are summarized below:
n=200∑x=15940∑x2=1271162 n = 200 \quad \sum x = 15940 \quad \sum x^2 = 1271162 n=200∑x=15940∑x2=1271162Find the mean and standard deviation of the sample.
Carry out a hypothesis test to test the engineer's suspicion at the 1% significance level. State your assumptions clearly.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.