widow widower - west virginia universitystat.wvu.edu/~rmnatsak/sol_review3-2.pdfreview #3-2 problem...

Review #3-2Problem #1. One prominent physician claims that 45% of those with lung cancer are

chain smokers. If the assertion is correct, find the probability that of20 such patientrecently admitted to a hospital, fewer than half are chain smokers. What is the expectednumber of chain smokers in the sample of 300 patients?

Problem #2. Ten is the average number of oil tankers arriving each day at a certainport city. The facilities at the port can handle at most 15 tankers per day. What is theprobability that on a given day tankers have to be turned away?

Problem #3. Compute a 98% confidence interval for the proportion of defectiveitems in a process when it is found that a sample of size 100 yields 8 defectives.

Problem #4. A commonly prescribed drug for relieving nervous tension is believed tobe only 60% effective. Experimental results with a new drug administered to a randomsample of 100 adults who were suffering from nervous tension show that 70 receivedrelief. Is this sufficient evidence to conclude that the new drug is superior to the onecommonly prescribed? Use a 0.05 level of significance.

Problem #5. An experiment was performed to compare the abrasive wear of twodifferent laminated materials. Twelve pieces of material 1 were tested by exposing eachpiece to a machine measuring wear. Ten pieces of material 2 were similarly tested. Ineach cases, the depth of wear was observed. The samples of material 1 gave an average(coded) wear of 85 units with a sample standard deviation of 4, while the samples ofmaterial 2 gave an average of 81 and a sample standard deviation of 5. Can we concludeat the 0.05 level of significance that the abrasive wear of material 1 exceeds that ofmaterial 2 by more than 2 units? Assume the populations to be approximately normalwith equal variances.

Problem #6. According to a Johns Hopkins University study, widows live longer thanwidowers. Consider the following survival data collected on 100 widows and 100widowers following the death of a spouse:

Years Lived Widow WidowerLess than 5 25 395 to 10 42 40More than 10 33 21

Can we conclude at the 0.05 level of significance that the proportions of widows andwidowers are equal with respect to the different time periods that a spouse survives afterthe death of his or her mate?

Problem #7. The grades of a class of 9 students on a midterm report, say X, and onthe final examination, say Y, are as follows:

(a) Estimate the linear regression line(b) Estimate the final examination grade of a student who received agrde of 85 on

the midterm report.

Problem #8. Let X be a continuous random variable with probability density functionf(x)= x/12.5 on the interval 1 < x < 5, and 0 otherwise.

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