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Unformatted text preview: 1 Exercises for Chapter 7 1. For a random sample of 50 measurements of the breaking strength of cotton threads, x = 210 grams and s = 18 grams. (a) Obtain an 80% confidence interval for the true mean breaking strength. What assump tions, if any, are needed for the validity of the confidence interval? (b) A 90% CI would be: WIDER LESS WIDE than the 80% CI. (Circle the correct answer.) (c) The interpretation of the CI you obtained in a) is: We are confident that 80% of all breaking strength measurements of cotton threads will be within the calculated CI. TRUE FALSE. (Circle one.) 2. A random sample of 25 engineering seniors is selected. The average amount of study time for this group turned out 15 hours/week with a sample standard deviation of 4 hours/week. Assume that the amount of study time of a randomly selected engineering student is normally distributed. (a) Construct a 98% CI for the true population mean. (b) Supposing that population standard deviation is known to be 4 hours/week, repeat part a. 3. Analysis of the venom of seven eightdayold worker bees yielded the following observations on histamine content in nanograms: 649 832 418 530 384 899 755 Use the following Minitab output when necessary to answer the following questions: N MEAN STDEV SE MEAN 90.0 PERCENT C.I. histmine 7 638.1 201.7 76.2 ( , ) (a) Compute a 90% confidence interval for the true average histamine content for all worker bees of this age. State the formula you are using. (b) Were any assumptions necessary to justify your computations? If so, list them. (c) Explain what 90% confidence means. 4. A question relating to a study of the echolocation system for bats is how far apart are the bat and an insect when the bat first senses the insect. The technical problems for measuring this are complex and so only 11 data points, Y 1 ,...,Y 11 , were obtained. It is given that 11 i =1 Y i = 532 and 11 i =1 Y 2 i = 29 , 000. Construct a 95% confidence interval for the mean distance . What assumption did you use? 5. A tire company wants to get a 99% CI for the true average lifetime, ( ), of a brand of tires. 10 tires are selected and tested on a test wheel that simulated normal road condition. The sample average lifetime is 41 (in thousands of miles), and the sample standard deviation is 3 . 59. (a) State the assumptions you make in order to construct a 99% confidence interval for . (b) Find a 99% confidence interval for the true average lifetime of the brand of tires, . 6. From twelve experiments it is found that the average amount of DDT causing 50% fatality in rainbow trout is 9.10 ppm with a standard deviation of 3.16 ppm....
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This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Pennsylvania State University, University Park.
 Fall '00
 Akritas

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