A precision automated nozzle dispenses a volume VVV ml of a chemical reagent, where VVV is modeled as a continuous random variable uniformly distributed on the interval [k−1.5,k+4.5][k - 1.5, k + 4.5][k−1.5,k+4.5], where kkk is a calibration constant.
A quality control audit takes a random sample of 80 dispensations, yielding a sample mean volume of vˉ=42.6\bar{v} = 42.6vˉ=42.6 ml.
Use the Central Limit Theorem to determine an approximate distribution for the sample mean volume Vˉ\bar{V}Vˉ.
Hence, find a 98% confidence interval for kkk. Give the limits of your interval to 3 significant figures.
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.