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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 a. What hypothesis is being tested if a jury commits a type I error by finding the firm guilty? practice b. What hypothesis is being tested if a jury commits a type II error by finding the firm guilty? Part (b) (5 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 a and B simultaneously. 4. If the null hypothesis is false, ß hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller β will be. 5. The power of a test is the probability of accepting Ho given that a specific alternative is true. is a maximum when the true value of a parameter approaches the Part (c) (4+4-8 marks) A manufacturer of sports equipment has developed a new synthetic fishing line that the company claims has a mean breaking strength of 8 kg with a standard devia the claim, a random sample of 25 lines is tested and found to have a mean breaking str standard deviation of (0.4 kg). Is the manufacturer claim justified at 0.1 level of significance?( state any ssumptions made) tion of 0.5 kg. To test ength of (7.8 kg) and a

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