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.
130 exam-style questions on AQA A Level Maths 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.