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.
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.