The net weight of industrial chemical canisters, WWW kg, follows a normal distribution with an unknown mean μ\muμ and a known standard deviation σ\sigmaσ. A logistical analysis of a random sample of 100 canisters resulted in a 95% confidence interval for μ\muμ of (74.14,75.46)(74.14, 75.46)(74.14,75.46).
Without performing any additional calculations, utilize this confidence interval to test the claim that μ=75.6\mu = 75.6μ=75.6. State the null and alternative hypotheses clearly and specify the significance level used for the test.
A separate random sample of 144 canisters was found to have a mean weight of 74.8574.8574.85 kg.
Determine a 98% confidence interval for μ\muμ based on this second sample.
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.