A high-precision semiconductor manufacturer claims that the mean etch depth, ddd nanometres, produced by their new 'Titan-X' laser system is greater than 120 nm. To investigate this claim, a quality control engineer measures the etch depth of a random sample of 16 etches and obtains the following summary statistics:
dˉ=123.6,s=7.2 \bar{d} = 123.6, \quad s = 7.2 dˉ=123.6,s=7.2The depth of the etches may be assumed to be normally distributed.
Stating your hypotheses clearly and using a 5% level of significance, test the claim made by the manufacturer.
The standard deviation of the etch depth for the previous generation 'Argon' laser system is 6.0 nm.
Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence that the variance of the etch depth for the Titan-X variety is different from that of the Argon variety.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.