A machine fills bottles with water. The amount of water in each bottle, W W\,W ml, is normally distributed with mean 500 ml. Given that 30% of bottles contain more than 504 ml
Find the value of k k\,k such that P(k<W<505)=0.45P(k < W < 505) = 0.45P(k<W<505)=0.45
The machine is adjusted so that the standard deviation of the amount of water in each bottle is now 6 ml. Following the adjustments the company manager now believes that the mean amount of water in each bottle is less than 500 ml. She takes a random sample of 20 bottles and finds the mean amount of water to be 498.1 ml. Test the company manager's belief at the 5% significance level. You should state your hypotheses clearly.
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.