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Math · Statistics And Probability
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02)- (2+5+8- 15 marks) Part (a) (2 marks) A large manufacturing firm is being charged with discrimination in its hiring practices. a. What hypothesis is being tested if a jury commits a type I error by finding the firm guilty? b. What hypothesis is being tested if a jury commits a type II error by finding the firm guilty? Part(b) (S marks) State whether the following statements true or false 1. The type I error and type II error are related. A increase in the probability of one generally results in an decrease in the probability of the other. 2. The size of the critical region, and therefore the probability of committing a type I error, can always be increased by adjusting the critical value(s). 3. A decrease in the sample size n will reduce α and β simultaneously. 4. If the null hypothesis is false, B is a maximum when the true value of a parameter approaches the hypothesized value. The greater the distance between the true value and the bypothesized value, the smaller will be. 5. The power of a test is the probability of accepting He given that a specific alternative is true. 8 marks) A manufacturer of sports equipment has developed a new synthetie fishing line that the company claims has a mean breaking strength of 8 kg with a standard deviation of 0.5 kg. To test the claim, a random sample of 25 lines is tested and found to have a mean breaking strength of (7.8 kg) and a standard deviation of (0.4 kg). Is the manufacturer claim justified at 0.1 level of significance?( state any assumptions made)

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