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.
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.