Introduction to Probability and Statistics for Engineers and Scientists

Problems 509

Test the hypothesis that the die is fair (that is, thatpi=^16 ,i=1,...,6)atthe

5 percent level of significance. Use the chi-square approximation.

3. Determine the birth and death dates of 100 famous individuals and, using the
   four-category approach of Example 11.2a, test the hypothesis that the death month
   is not affected by the birth month. Use the chi-square approximation.


4. It is believed that the daily number of electrical power failures in a certain
   Midwestern city is a Poisson random variable with mean 4.2. Test this hypothesis
   if over 150 days the number of days havingipower failures is as follows:

Failures Number of Days

00

15

222

323

432

522

619

713

86

94

10 4

11 0

5. Among 100 vacuum tubes tested, 41 had lifetimes of less than 30 hours, 31 had
   lifetimes between 30 and 60 hours, 13 had lifetimes between 60 and 90 hours,
   and 15 had lifetimes of greater than 90 hours. Are these data consistent with the
   hypothesis that a vacuum tube’s lifetime is exponentially distributed with a mean
   of 50 hours?


6. The past output of a machine indicates that each unit it produces will be

top grade with probability .40

high grade with probability .30

medium grade with probability .20

low grade with probability .10

A new machine, designed to perform the same job, has produced 500 units with

the following results.