Introduction to Probability and Statistics for Engineers and Scientists

Problems 513

Defective Acceptable Superior

Before 25 218 22

After 9 103 14

Is this change significant at the .05 level?

21.A sample of 300 cars having cellular phones and one of 400 cars without phones

were tracked for 1 year. The following table gives the number of these cars involved

in accidents over that year.

Accident No Accident

Cellular phone 22 278

No phone 26 374

Use the above to test the hypothesis that having a cellular phone in your car

and being involved in an accident are independent. Use the 5 percent level of

significance.

22.To study the effect of fluoridated water supplies on tooth decay, two communities

of roughly the same socioeconomic status were chosen. One of these communities

had fluoridated water while the other did not. Random samples of 200 teenagers

from both communities were chosen, and the numbers of cavities they had were

determined. The following data resulted.

Cavities Fluoridated Town Nonfluoridated Town

0 154 133

120 18

214 21

3 or more 12 28

Do these data establish, at the 5 percent level of significance, that the number

of dental cavities a person has is not independent of whether that person’s water

supply is fluoridated? What about at the 1 percent level?

23.To determine if a malpractice lawsuit is more likely to follow certain types of

surgery, random samples of three different types of surgeries were studied, and the

following data resulted.

Type of Operation Number Sampled Number Leading to a Lawsuit

Heart surgery 400 16

Brain surgery 300 19

Appendectomy 300 7