STAT 201 Final, Spring 2008

AMERICAN UNIVERSITY OF BEIRUT MATH 207 FINAL EXAMINATION —” Part I: Multiple choice ; Aids allowed: One 8.5” x 11” formula sheet, calculator, Z, and t tables. 1. Erin is a runner who keeps accurate records of her training. In one season she averaged 3.4 miles per day with a standard deviation of .5 miles. What is her standard deviation in’kilometers? (1 mile=1.6 kilometers) ‘ ‘ (a) .50 kilometers (b) .80 kilometers (c) 1.60 kilometers (d) 3.40 kilometers (e) none of the above . In a population of students, the number of calculators owned is a random variable X with P(X = 0) = .2, P(X = 1) = .6, and P(X = 2) =.2. The mean of this probability distribution is e) the answer cannot be computed from the information given . Refer to previous problem. The standard deviation for this probability distribution is ; (a) .40 (b) .63 (c) 1 (d) .36 (e) the answer cannot be computed from the above information (yreRtcas Net Hse | . You want to compute a 90% confidence ‘interval for the mean of a population with unknown standard ‘deviation. The sample size is 30. The value of t* you would use for this interval is 1.96 ; . . A 95% confidence interval for the mean reading achievement score for a population of third grade students is (44.2, 54.2). The margin of error of this interval is (a) 10 (b) 5 a (c) 2.5 (d) 95% (e) The answer cannot be determined from the information given. . Refer to previous problem. The sample mean is (a) 44.2 (b) 54.2 - (c) .95 (d) 49.2 (e) The answer cannot be be determined from the above information, to 7. A copy machine dealer has data on the number z of copy machines at each of 89 customers locations and the number y of service calls in a month at each location. Summary calculations give 2 = 747.60, yx? = 6667.92, © y = 1263.80, Sy? = 19216.68, and 3° zy = 11219.85. What is the slope of the least squares regression line of number of ser- vice calls on number of copiers? . . none of these e) can’t tell from the information given. . In the setting of the previous problem, about what percent of the vari- ation in the number of service calls'is explained by the linear relation between number of service calls and number of machines? ' Part II (please, show your work) 9. Assume that 10% of a population of electronic components are defec- tive. A random sample of n = 500 is drawn from this population. (a) Give the mean and standard deviation for the proportion of de- fectives in the sample. (b) What is an approximate value for the probability that the propor- tion of defectives is greater than -1? (c) What is an approximate value for the probability that the number of defectives is less than 40? 10. A study is performed to investigate the. relationship between college and high school grade point averages. A simple linear regression is used to predict the first year grade point average of college students using their high school grade point average. A sample of 100 students is used for the study. The equation of the least squares line fit to the data is 7 = 1.24 + .652. (a) Give an interpretation for the slope of the line under the above setting. (b) If the standard error of the slope is .04, find the 95% confidence interval for the true slope of the line. (c) Test the hypothesis that the slope is zero versus that it is positive. Give the test statistic, an approximate P-value, and state your conclusion.