An automated laboratory sensor measures the concentration CCC of a specific solution in parts per million (ppm). The readings follow a normal distribution with mean μ\muμ. For the analysis to be considered highly precise, the deviation from the mean should be strictly controlled such that the probability of a reading exceeding the mean by more than 12 ppm is exactly 0.005; that is P(C>μ+12)=0.005P(C > \mu + 12) = 0.005P(C>μ+12)=0.005.
Show that this precision requirement implies a standard deviation of 4.659 ppm, to 3 decimal places.
A quality control technician suspects the sensor is calibrated incorrectly and is over-reporting the concentration. A random sample of 10 readings is taken, yielding the following results:
253.2,250.5,256.8,251.4,253.1,250.8,255.1,257.0,248.9,255.2 253.2, 250.5, 256.8, 251.4, 253.1, 250.8, 255.1, 257.0, 248.9, 255.2 253.2,250.5,256.8,251.4,253.1,250.8,255.1,257.0,248.9,255.2Assuming the population standard deviation is 4.659 ppm, test at the 1% significance level whether the mean concentration being measured is greater than 250 ppm. State your hypotheses 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.