A cosmic ray observatory monitors the frequency of high-energy solar micro-bursts. Records show that the observatory detects an average of 48 micro-bursts per 10-hour cycle. The number of micro-bursts detected per hour is modeled using a Poisson distribution.
Determine the critical region for a two-tailed test of the mean number of detections per hour at a 10% level of significance. The probability of rejection in each tail must be less than 0.05.
Calculate the actual significance level of this test.
A new filtering lens is installed which the lead scientist claims has significantly reduced the sensitivity to these micro-bursts, thereby reducing the mean number of detections.
A random observation period of 50 hours is conducted, and a total of 215 micro-bursts are recorded.
Use a suitable approximation to test the scientist's claim at a 5% level of significance. You should state your hypotheses clearly.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.