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.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.