Statistics Homework Solutions 52

Statistics Homework Solutions 52 - 52 CHAPTER 2 35(a If the...

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Unformatted text preview: 52 CHAPTER 2 35. (a) If the pooled test is negative, it is the only test performed, so X 1. If the pooled test is positive, then n additional tests are carried out, one for each individual, so X n 1. The possible values of X are therefore 1 and n 1. ¡ ¢ ¡ ¢ (b) The possible values of X are 1 and 5. Now X 1 if the pooled test is negative. This occurs if none of the individuals has the disease. The probability that this occurs is 1 0 1 4 0 6561. Therefore P X 1 0 6561. It follows that P X 5 0 3439. So µX 1 0 6561 5 0 3439 2 3756. ¡ ¡¥ ¡ ¤ ¨ ¡ ¥¨ ¤ ¡ ¨ ¡¥ ¡¥ ¨ ¡ ¤ ¨ ¨ ¤ ¢¥ ¨ ¤ ¡ (c) The possible values of X are 1 and 7. Now X 1 if the pooled test is negative. This occurs if none of the individuals has the disease. The probability that this occurs is 1 0 2 6 0 262144. Therefore P X 1 0 262144. It follows that P X 7 0 737856. So µX 1 0 262144 7 0 737856 5 4271. ¡ ¡¥ ¡ ¤ ¨ ¡ ¥¨ ¤ ¡ ¨ ¡¥ ¨ ¡ ¡¥ ¤ ¨ ¨ ¤ ¢¥ ¨ ¤ ¡ (d) The possible values of X are 1 and n 1. Now X 1 if the pooled test is negative. This occurs if none of the individuals has the disease. The probability that this occurs is 1 p n . Therefore P X 1 1 p n . It n. 11p follows that P X n 1 So µX 1 1 p n n 1 1 1 p n n 1 n 1 p n. ¡ ¤ ¡¥ ¡ ¤ ¥ ¡ ¢ ¤ ¥ ¥ 10. Solving for p yields p ¡ ¡ 10 0 2057. ¨ ¤ ¡ ¥ p ¡ ¢ ¡ ¡ 10 1 ¥ ¤ ¡ ¡¥¥ ¤ ¡ ¡ ¤ ¡¥ ¡ ¡ ¤¥ ¢ ¢ ¡ ¤ ¢ ¤ ¥ ¡ ¤ ¡ (e) The pooled method is more economical if 11 ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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