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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.