The hourly count of particulate matter particles P P\,P detected by an atmospheric monitoring sensor follows a Poisson distribution with a mean of 8.4.
A random sample of 50 hours is recorded, and the mean number of particles per hour, Pˉ\bar{P}Pˉ, is calculated.
Specify the approximate distribution for the mean number of particles detected per hour for a random sample of 50 hours.
The hourly count of specific deep-space radio pulses detected by a telescope follows a Poisson distribution with mean μ\muμ.
A random sample of 80 hours of observation is taken and the sample mean count, Sˉ\bar{S}Sˉ, is determined. The width of the 95% confidence interval for μ \mu\,μ is calculated to be 1.2.
Find an estimate for the value of μ\muμ.
A researcher conducts two further independent observation runs of 80 hours each and calculates a 95% confidence interval for μ \mu\,μ for each run.
Determine the probability that the true mean μ \mu\,μ is contained within exactly one of these two new confidence intervals.
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.