A research drone measures the atmospheric pressure at a specific altitude. The pressure PPP, in suitable units, is modeled as a continuous random variable having a uniform distribution on the interval [α−3,α+9][\alpha - 3, \alpha + 9][α−3,α+9], where α\alphaα is a constant relating to the specific layer of the atmosphere. A random sample of nnn independent observations of PPP is collected, where nnn is large.
Apply the Central Limit Theorem to find an approximate distribution for the sample mean Pˉ\bar{P}Pˉ. Give your answer in terms of nnn and α\alphaα where appropriate.
The nnn observations have a sample mean of 85.585.585.5. Given that the upper limit of the 98%98\%98% confidence interval for α\alphaα is 82.732682.732682.7326,
calculate the value of nnn. Show your working clearly.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.