A research drone measures the atmospheric pressure at a specific altitude. The pressure $P$ , in suitable units, is modeled as a continuous random variable having a uniform distribution on the interval $[α−3,α+9][\alpha - 3, \alpha + 9]$ , where $α\alpha$ is a constant relating to the specific layer of the atmosphere. A random sample of $n$ independent observations of $P$ is collected, where $n$ is large.

Apply the Central Limit Theorem to find an approximate distribution for the sample mean $Pˉ\bar{P}$ . Give your answer in terms of $n$ and $α\alpha$ where appropriate.

The $n$ observations have a sample mean of $85.5$ . Given that the upper limit of the $98%98\%$ confidence interval for $α\alpha$ is $82.7326$ ,

calculate the value of $n$ . Show your working clearly.

Apply the Central Limit Theorem to find an approximate distribution for the sample mean $Pˉ\bar{P}$ . Give your answer in terms of $n$ and $α\alpha$ where appropriate.

The $n$ observations have a sample mean of $85.5$ . Given that the upper limit of the $98%98\%$ confidence interval for $α\alpha$ is $82.7326$ ,

calculate the value of $n$ . Show your working clearly.

2.5 O: Statistical hypothesis testing

Question 58

Markscheme

2.5 O: Statistical hypothesis testing

Question 58

Markscheme

2.5 O: Statistical hypothesis testing

Question 58

2.5 O: Statistical hypothesis testing Questions

2.5 O: Statistical hypothesis testing

Question 58

2.5 O: Statistical hypothesis testing Questions