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.
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.