Tackle the questions attached below..
Explain the difference between the paired t-test and the two-sample t-test Trendy Tyres Ltd. Has introduced a new brand of tyres which in their advertisements claim to be superior to their only competitor brand. The Roadmaster Tyres. The brand manager of Roadmaster Tyres disputes this claim which he says is an advertisement gimmick. The brand managers of the two companies agree to run a road test for the brands. Ten (10) saloon cars of uniform weight and identical specifications are to be used for the test. Each car is fitted with both brands of tyres: One brand at the front the other brand at the rear. The cars cover a distance of 5,000 kilometers and the trend wear is recorded as follows: Trend tyres Roadmaster tyres centimeters Centimeters 1.08 1.12 1.06 1.09 1.24 1.16 1.20 1.24 1.17 1.23 1.21 1.25 1.18 1.20 1.10 1.15 1.22 1.19 1.60 1.13 Required: i) Determine whether Trendy Tyres Ltd.'s claim is true using a = 0.01 ii) What are the assumptions you have made in (i) above?a) Explain what is meant by the following terms as used in statistical inference: i) Statistical hypothesis; ii) Test of a hypothesis; iii) Type I error; iv) Type II error; v) Level of significance b) Cross Lines Group (CLG) has two factories in different parts of the country. Their Resources, including the labor force skills are regarded as identical and both factories Were built at the same time. A random sample of output data during a given period has been taken from each factory and converted to standard hours of output per employee. The data are given below: Factory 1 42 50 43 39 41 49 52 41 46 48 Factory 2 39 45 36 6 42 52 37 43 41 40 39 You are given that for factory 1 mean = 45.1 and variance = 20.10 and that for factory 2 mean = 41.4 and variance = 21.16. Required: i) Test the hypothesis that the mean standard hours for employees in the two factories is the same. ii) Comment briefly on the conditions of the test and interpret the outcome.a) State clearly what is meant by two events being statistically independent. b) In a certain factory which employs 500 men, 2% of all employees have a minor accident in a given year. 0fthcse. 30% had safety instructions whereas 30% of all employees had no Required Find the probability of an employee being accident-tree given that he had: i) No safety instructions ii) Safety instructions c) An electric utility company has found that the weekly number of occurrences of lightning striking the transformers is a Poisson distribution with mean 0.4. Required: i) The probability that no transformer will be struck in a week. ii) The probability that at most two transformers will be struck in a week
