The yield of a synthetic polymer SSS, measured in milligrams, is modeled by a continuous uniform distribution on the interval [c−10,c+20][c - 10, c + 20][c−10,c+20], where c c\,c is a controlled reaction constant. A large random sample of n n\,n yields is taken during a production run.
Use the Central Limit Theorem to determine an approximate distribution for the sample mean Sˉ\bar{S}Sˉ. Give the parameters of the distribution in terms of n n\,n and c c\,c where appropriate.
The sample mean of the n n\,n observations is recorded as 152.4. Given that the upper bound of a 95% confidence interval for the constant ccc, based on this sample, is 147.89,
calculate the value of nnn. Show your working 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.