A factory produces packets of cereal. The weight of cereal in each packet, W W\,W g, is normally distributed with mean 400 g. Given that 20% of packets contain more than 405 g.
Find the value of k k\,k such that P(k<W<410)=0.50P(k < W < 410) = 0.50P(k<W<410)=0.50.
The production process is adjusted so that the standard deviation of the weight of cereal is now 6 g. Following the adjustments, the quality control manager believes that the mean weight of cereal in each packet is less than 400 g. She takes a random sample of 25 packets and finds the mean weight to be 397.5 g. Test the manager's belief at the 5% significance level. You should state your hypotheses clearly.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.