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Question 1: Estimation and Hypothesis Tests-One Population. Part I. (20 Marks) An IQ test was administered to twelve students and the scores were as follows: 1 Student IQ score 2 102 3 94 4 81 5 115 6 75 7 74 8 116 9 98 10 114 11 96 12 100 87 Assume that IQ is normally distributed with mean u and variance 02. 1. If o2=196, construct a 95% confidence interval foru, the true mean IQ in the population. (5 Marks) 2. What sample size is necessary to ensure an interval width w= 10? (5 Marks) 3. Now consider o2 unknown. Is the claim that u is less than 100 justified? Perform a test at the a=0.10 level of significance, by the following 5 steps: (10 Marks) Step 1. Hypotheses and significance level: Ho: Ha: Step 2. Test Statistic and its sampling distribution under Ho: Step 3. Observed value of the test statistic: Step 4. P-value under Ho: Step 5. Decision and conclusion (interpretation of the result): a=

Part II. (15 Marks) In an initial drugs test, 5.8% of job applicants tested negative. It is claimed that now the rate is lower. A random sample of 1520 current job applicants ended in 58 negative results. 1. Construct a 95% confidence interval for p, the true proportion of negative results in the population (classical form). (5 Marks) 2. Conduct a statistical test of hypothesis on this claim at the 0.01 level of significance, by the same 5 steps as above. (10 Marks)