Statistics Questions & Answers

Statistics Questions & Answers A company claims that a quarter of the bolts sent to them are faulty. To test this claim the number of faulty bolts in a random sample of 50 is recorded. Give two reasons why a binomial distribution may be a suitable model for the number of faulty bolts in the sample. (2 marks) - ANSWER: • Each bolt is either faulty or not faulty. • The probability of a bolt being faulty (or not) may be assumed constant. • Whether one bolt is faulty (or not) may be assumed to be independent (or does not affect the probability of) whether another bolt is faulty (or not). • There is a fixed number (50) of bolts. • A random sample. A factory produces shopping bags for a large supermarket chain. The breaking load of a bag is the maximum load that it can carry before it breaks. The supermarket chain places an order for 50 000 shopping bags but wishes to know the breaking load of the bags. Suggest two reasons why a census would be unsuitable for this purpose.(2 marks) - ANSWER: • There are a very large number of bags • Bags are tested to destruction - there would be no bags left A manufacturer claims that more than 55% of its batteries last for at least 15 hours of continuous use. To test the manufacturer's claim, a random sample of 300 batteries were tested. State the hypotheses for a one-tailed test of the manufacturer's claim.(1 mark) - ANSWER: H0: p = 0.55 H1: p > 0.55