The hydrostatic head (a measure of water resistance) of fabric treated with 'HydroGuard' is normally distributed with a standard deviation of 450 mm. A quality control check of 25 samples from Production Line X found a mean hydrostatic head of 3200 mm.
Determine a 98% confidence interval for the mean hydrostatic head of fabric from Production Line X.
An independent sample of 30 items from Production Line Y yielded a mean hydrostatic head of 3450 mm. An engineer suggests that the mean resistance of fabric from Line Y is higher than that of Line X.
By clearly stating your hypotheses, test the engineer's suggestion at the 1% level of significance.
The regulatory standard for this fabric is a mean hydrostatic head of μ\muμ mm. When looking at the two production lines individually, at the 1% significance level, there is insufficient evidence to conclude that the mean resistance of Line X is less than μ\muμ, and insufficient evidence to conclude that the mean resistance of Line Y is less than μ\muμ.
Calculate the maximum possible value of μ\muμ, giving your answer to the nearest integer.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.