Introduction to Probability and Statistics for Engineers and Scientists

Problems 417

1996 % GraduatesTaking

Verbal Math SAT

Rhode Island............ 501 491 69

South Carolina.......... 480 474 57

South Dakota........... 574 566 5

Tennessee............... 563 552 14

Texas................... 495 500 48

Utah................... 583 575 4

Vermont................ 506 500 70

Virginia................. 507 496 68

Washington............. 519 519 47

West Virginia........... 526 506 17

Wisconsin.............. 577 586 8

Wyoming............... 544 544 11

National Average......... 505 508 41

Source: The College Board

8. Verify Equation 9.3.3, which states that

Var(A)=

σ^2

∑n

i= 1

xi^2

n

∑n

i= 1

(xi− ̄x)^2

9. In Problem 4,
   (a) Estimate the variance of an individual response.
   (b) Determine a 90 percent confidence interval for the variance.
   10.Verify that

SSR=

SxxSYY−S^2 xY

Sxx

11.The following table relates the number of sunspots that appeared each year from

1970–1983 to the number of auto accident deaths during that year. Test the

hypothesis that the number of auto deaths is not affected by the number of

sunspots. (The sunspot data are from Jastrow and Thompson,Fundamentals and

Frontiers of Astronomy,and the auto death data are fromGeneral Statistics of the U.S.

1985.)