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University of Illinois, Urbana ChampaignBIOE 505final_with_answers

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BIOE 505 Final Exam Name: 1. (10 points) A random sample of size ?ଵ ൌ 16 is selected from a normal population with a mean of 80 and a standard deviation of 12. (A) Find the probability that th... e sample mean ത?തଵത is less than 70. Answer:                                               1 1 1 1 80 80 80 70 3.33 3.33 1 3.33 12 12 12 16 16 16 1 0.999571 0.000429 X X X P X P P P By the table it is 1-0.999566=0.000434. (B) Now a second random sample of size ?ଶ ൌ 25 is taken from another normal population with a mean of 70 and a standard deviation of 10. Let ത?തଵത and ത?തതଶത be the two sample means. Find the probability that ത?തଵത െ ? തതതଶത exceeds 6. Answer: Let    X X X 1 2 denote the sample difference, which approximately follows normal distribution with mean equal to 80-70=10 and standard deviation 12 10 2 2 3.606 16 25     . Using z-table, we could find                     10 6 1.109 1.109 0.866 3.606 X P X P P Z 2. (5 points) A data set collected in Queen Elizabeth Hospital, Birmingham (Andrews and Herzberg (1985)) provides the results of analysis of 20 samples of serum measured for their sodium content. The sample mean is 140.55ppm and the sample standard deviation is 9.445ppm. At 5% significance level, is there evidence that the mean level of sodium in this serum is different from 140 ppm? Use the statistic based on the normal distribution for your answer. Answer: We use the two-sided hypothesis test 0 1 : 140 : 140 H H          . The sample mean is 140.55 and the sample standard deviation 9.445. The z-statistic is    140.55 140 0.26 9.445 20 Z and the p-value is 0.79. At α=5% significance level zα/2=1.96>Z. Thus we cannot reject the null hypothesis [Show More]

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