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THE UNIVERSITY OF NEW SOUTH WALES DEPARTMENT OF STATISTICS Exercises for MATH3811, Statistical Inference One Sample Problems. Two Sample Problems 1. In a study of drug abuse in a suburb A it was found that the median I.Q. of arrested abusers who were 16 years of age or older was 107. In order to test whether the median I.Q. of arrested abusers aged 16 or more in another suburb B is also 107, the I.Q.'s of 12 such persons from the suburb B were determined and are given below: 108, 111, 99, 127, 109, 100, 90, 94, 135, 104, 119, 117 a) Carry out an appropriate sign test. b) Give a non-parametric point estimate and find 95% confidence limits for the median I.Q. of drug abusers aged 16 or more in the suburb B. 2. The following table gives the level of the chemical serotonin in the blood of a patient before and after injecting 2.5mg of the drug reserpine. Patient 1 2 3 4 5 6 7 8 9 10 Level before 0.61 0.59 0.68 0.67 0.70 0.56 0.64 0.59 0.64 0.64 Level after 0.56 0.46 0.59 0.53 0.79 0.50 0.54 0.52 0.72 0.60 a) Carry out a sign test of the hypothesis that there is no difference in the serotonin level of a patient before and after injecting reserpine.

- another suburb
- alcohol treatment
- wilcoxon test
- who lived
- pure alcohol
- boy
- patient before
- exact wilcoxon
- test whether
- random variable

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THE UNIVERSITY OF NEW SOUTH WALES

DEPARTMENT OF STATISTICS

Exercises for MATH3811, Statistical Inference

One Sample Problems.Two Sample Problems

1. Ina study of drug abuse in a suburb A it was found that the median I.Q. of arrested abusers who were 16 years of age or older was 107.In order to test whether the median I.Q. of arrested abusers aged 16 or more in another suburb B is also 107, the I.Q.’s of 12 such persons from the suburb B were determined and are given below: 108, 111, 99, 127, 109, 100, 90, 94, 135, 104, 119, 117 a) Carryout an appropriate sign test. b) Givea non-parametric point estimate and ﬁnd 95% conﬁdence limits for the median I.Q. of drug abusers aged 16 or more in the suburb B.

2. Thefollowing table gives the level of the chemical serotonin in the blood of a patient before and after injecting 2.5mg of the drug reserpine. Patient 1 2 3 4 5 6 7 8 910 Level before0.61 0.59 0.68 0.67 0.70 0.56 0.64 0.59 0.64 0.64 Level after0.56 0.46 0.59 0.53 0.79 0.50 0.54 0.52 0.72 0.60

a) Carryout a sign test of the hypothesis that there is no diﬀerence in the serotonin level of a patient before and after injecting reserpine.What assumptions need to be made to carry out the test? b) Alsocarry out a Wilcoxon signed rank test of the same hypothesis stating the assumptions needed to be made for the test to be valid.

3. Apsychological experiment was conducted to compare the length of response time (in seconds) for two diﬀerent stimuli.In order to remove natural person-to person variability in the responses both stimuli were applied to each of nine subjects, thus permitting an analysis of the diﬀerence between stimuli within each person. Subject 12 34 5 67 8 9 Stimulus 19.4 7.8 5.6 12.1 6.9 4.28.8 7.7 6.4 Stimulus 210.3 8.9 4.1 14.7 8.7 7.1 11.3 5.2 7.8 Use the sign test to determine whether suﬃcient evidence exists to indicate a diﬀerence in mean response for the two stimuli.State the actual level of signiﬁcance of your test.

4. Ina controlled environment laboratory, ten men and ten women were tested to determine the room temperature they found to be most comfortable.The results were as follows: Men: 74 72 77 76 76 73 75 73 74 75 Women: 75 77 78 79 77 73 78 79 78 80 Stating the assumptions you need to make, carry out a Wilcoxon test of the hypothesis that the average comfortable temperature is the same for men and women.State the exact level of signiﬁcance of your test procedure.

5. Inan annual survey to determine whether state pay scales were commensurate with private sector salaries, government and private workers were matched as closely as possible (with respect to the type of job, educational background, years experience, etc.)and the salaries of the matched pairs were obtained.The data in the table are the annual salaries for 12 such matched pairs:

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