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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.