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HW5Solution

# HW5Solution - Geostatistics Petroleum and Geosystems...

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Geostatistics Petroleum and Geosystems Engineering 337 (19065) Spring 2008 Homework Assignment #5 Section 5.1 – Page 335 1. Find the value of 2 / α z to use in expression (5.1) to construct a confidence interval with level a. 95% Ans 96 . 1 025 . 0 2 / , 05 . 0 , 1 % 95 025 . 0 2 / = = = = = z z then Hence b. 98% Ans 33 . 2 01 . 0 2 / , 02 . 0 , 1 % 98 01 . 0 2 / = = = = = z z then Hence c. 99% Ans 58 . 2 57 . 2 005 . 0 2 / , 01 . 0 , 1 % 99 005 . 0 2 / or z z then Hence = = = = = d. 80% Ans

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28 . 1 1 . 0 2 / , 2 . 0 , 1 % 80 1 . 0 2 / = = = = = z z then Hence α 2. Find the levels of the confidence intervals that have the following values of 2 / z : a. 96 . 1 2 / = z Ans % 95 ) 025 . 0 ( 2 1 % , 025 . 0 2 / , 9750 . 0 96 . 1 2 / = = = = confidence Therefore Hence is z Area b. 17 . 2 2 / = z Ans % 97 ) 015 . 0 ( 2 1 % , 015 . 0 2 / , 9850 . 0 17 . 2 2 / = = = = confidence Therefore Hence is z Area c. 28 . 1 2 / = z Ans % 80 ) 10 . 0 ( 2 1 % , 10 . 0 2 / , 90 . 0 8997 . 0 28 . 1 2 / = = = = confidence Therefore Hence or is z Area d. 28 . 3 2 / = z Ans
% 9 . 99 ) 0005 . 0 ( 2 1 % , 0005 . 0 2 / , 9995 . 0 28 . 3 2 / = = = = confidence Therefore Hence is z Area α

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7. In a random sample of 100 batteries produced by a certain method, the average lifetime was 150 hours and the standard deviation was 25 hours. a. Find a 95% confidence interval for the mean life-time of batteries produced by this method. Ans Given 100 25 150 = = = n s X 90 . 154 150 ) 100 / 25 ( * 96 . 1 / 96 . 1 , 96 . 1 , 96 . 1 05 . 0 1 1 2 1 2 / 05 . 0 2 / = + = = + = = = c c n s X c Hence z z α Do the same for z = -1.96 10 . 145 / 96 . 1 2 2 2 = = c n s X c Hence, 95% confidence that the population mean is in the interval [] 90 . 154 , 10 . 145 b. Find a 99% confidence interval for the mean life-time of batteries produced by this method. Ans 45 . 156 150 ) 100 / 25 ( * 58 . 2 / 58 . 2 , 58 . 2 , 58 . 2 01 . 0 1 1 2 1 2 / 01 . 0 2 / = + = = + = = = c c n s X c Hence z z Do the same for z = -2.58
55 . 143 / 58 . 2 2 2 2 = = c n s X c Hence, 99% confidence that the population mean is in the interval [] 45 . 156 , 55 . 143 c. An engineer claims that the mean lifetime is between 147 and 153 hours. With what level of confidence can this statement be made? Ans % 98 . 76 % 1 % % ) 1151 . 0 ( * 2 ; 1151 . 0 20 . 1 ) 100 / 25 ( 150 147 ) / ( 147 2 / 2 / 2 2 / 2 2 / = = = = + = + = α confidence Hence is z Area z z n s z X d. Approximately how many batteries must be sampled so that a 95% confidence interval will specify the mean to within +/- 2 hours? Ans The level is 95%, so that = 0.05 and 2 / z = 1.96. The value of s is 25. Hence, 601 ~ 2 ) / )( ( 2 / n n s z = e. Approximately how many batteries must be sampled so that a 99% confidence interval will specify the mean to within +/- 2 hours? Ans The level is 99%, so that = 0.01 and 2 / z = 2.58. The value of s is 25. Hence, 1041 ~ 2 ) / )( ( 2 / n n s z =

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8. In a random sample of 53 concrete specimens, the average porosity (in %) was 21.6 and the standard deviation was 3.2. a. Find a 90% confidence interval for the mean porosity of specimens of this type of concrete.
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HW5Solution - Geostatistics Petroleum and Geosystems...

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