Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript

The Islamic University of Gaza Faculty of Engineering Department of Civil Engineering 9/1/2010 Statistics and Probability for Engineering Applications ENGC 6310 - Dr. Samir Safi Practice Problems for Chapter 13 & 14 Solution 1- A die is tossed 180 times with the following results: x 1 2 3 4 5 6 f 28 36 36 30 27 23 Is this a balanced die? Use a 0.01 level of significance. 2- In 100 tosses of a coin, 63 heads and 37 tails are observed. Is this a balanced coin? Use a 0.05 level of significance. 1 3- A random sample of 90 adults is classified according to gender and the number of hours they watch television during a week: Watching Gender Television Male Female Over 25 hours 15 29 Under 25 27 19 hours Use a 0.01 level of significance and test the hypothesis that the time spent watching television is independent of whether the viewer is male or female. 4- The following responses concerning the standard of living at the time of an independent opinion poll of 1000 households versus one year earlier seems to be in agreement with the results of a study published in Across the Board (June 1981): Period Standard of Living Somewhat Better Same Good 1980: Jan. 72 144 84 May 63 135 102 Sep. 47 100 53 1981: Jan. 40 105 55 Test the hypothesis that the proportions of households within each standard of living category are the same for each of the four time periods. Use a P-value. 2 5- The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: x 77 50 71 72 81 94 96 99 67 y 82 66 78 34 47 85 99 99 68 (a) Estimate the linear regression line. (b) Estimate the final examination grade of a student who received a grade of 85 on the midterm report. 3 6- In a certain type of metal test specimen, the normal stress on a specimen is known to be functionally related to the shear resistance. The following is a set of coded experimental data on the two variables: Normal Stress, X Shear Resistance, Y 26.8 26.5 25.4 27.3 28.9 24.2 23.6 27.1 27.7 23.6 23.9 25.9 24.7 26.3 28.1 22.5 26.9 21.7 27.4 21.4 22.6 25.8 25.6 24.9 (a) Estimate the regression line (b) Estimate the shear resistance for a normal stress of 24.5 kilograms per square centimeter. 4