RYERSON UNIVERSITY FACULTY OF ENGINEERING, ARCHITECTURE & SCIENCE

DEPARTMENT OF CHEMICAL ENGINEERING

CHE 331 Engineering Statistical Design

Assignment # 4 (Due on March 31, 2015)

Problem # 1 (Problem # 8-89)

The tar content in 30 samples of cigar tobacco follows:

1.542 1.585 1.532 1.466 1.499 1.611

1.622 1.466 1.546 1.494 1.548 1.626

1.440 1.608 1.520 1.478 1.542 1.511

1.495 1.533 1.532 1.523 1.397 1.487

1.598 1.498 1.600 1.504 1.545 1.558

(a) Is there evidence to support the assumption that the tar content is normally

distributed?

(b) Find a 99% CI on the mean tar content

(c) Find a 99% prediction interval on the tar content for the next observation that will

be taken on this particular type of tobacco

(d) Find an interval that will contain 99% of the values of the tar content with 95%

confidence

(e) Explain the difference in the three intervals computed in parts (b), (c) and (d)

Problem # 2

A CI is desired for the true average stray-load loss µ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 3.0.

a. Compute a 95% CI for µ when n = 25 and x = 60. b. Compute a 95% CI for µ when n = 100 and x = 60. c. Compute a 99% CI for µ when n = 100 and x = 60. d. Compute an 82% CI for µ when n = 100 and x = 60. e. How large must n be if the width of the 99% interval for µ is to be 1.0?

Problem # 3

Determine the following: a. The 90th percentile of the chi-squared distribution with ν = 12. b. The 10th percentile of the chi-squared distribution with ν = 12. c. 2(10.98 36.78)P χ≤ ≤ where 2χ is a chi-squared rv with ν = 22. d. 2 2( 14.611 or 37.652)P χ χ< > where 2χ is a chi-squared rv with ν = 25