An industrial manufacturer claims that an automated process fills double-glazing window units with a mean volume of 500 ml of argon gas. An environmental inspector suspects that the units are being underfilled. During an audit, a random sample of 60 units is tested, yielding a sample mean volume of 498.2 ml and a standard deviation of 7.5 ml.
Test the inspector's suspicion at a 5% level of significance. State your hypotheses clearly.
Construct a 98% confidence interval for the mean volume of argon gas in the window units from this production line.
Based on your results from parts (a) and (b), suggest what advice should be given to the manufacturer regarding their filling process.
The manufacturer recalibrates the machinery, which results in a new unknown mean volume μ\muμ and a reduced standard deviation of 4.0 ml. Assume that the volumes in individual units after recalibration are normally distributed. A researcher plans to take a sample of size nnn and use the sample mean Vˉ\bar{V}Vˉ as an estimator of μ\muμ.
Calculate the minimum value of nnn required such that P(∣Vˉ−μ∣<0.8)≥0.95P(|\bar{V} - \mu| < 0.8) \ge 0.95P(∣Vˉ−μ∣<0.8)≥0.95.
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.