Engineering Statistics Review For Exam (Page 3 of 4) in pdf

Problem #6

The Milk for the People dairy has developed a line of lactose-free products for individuals who

have trouble digesting regular milk and milk-products. To assess the potential market for the

lactose-free line, Milk for the People conducted a survey.

In a random sample of 250

individuals, 86 had trouble digesting regular milk products.

A. Construct a 99% confidence interval for the proportion of all individuals who have trouble

digesting milk products, USING THE APPROPRIATE STEPS.

B. One executive at Milk for the People wants to issue a press release for the debut of their new

products in which it is stated that “35% of all individuals have trouble digesting milk

products”. Is this statement consistent with your CI result from part A? EXPLAIN.

C. Milk for the People could only afford to survey 250 people.

i. How large is the margin of error for your CI in Part A? _______

ii. What sample size would be needed to estimate the proportion of all individuals who

have trouble digesting milk products within 0.03 with 99% confidence? SHOW

YOUR WORK!

Problem #7

The Environmental Protection Agency sets a limit of five parts per million (ppm) on PCB (a

dangerous substance) in water. A local manufacturing firm discharges small amounts of PCB

into the Genesee River. Specimens of river water are obtained regularly to moniter the PCB

level. If a sample indicates that the mean amount of PCB exceeds 3 ppm, production will be

halted to prevent an environmental hazard.

A. State the hypotheses to be tested.

B. A random sample of 50 water specimens was collected with a probability value of 0.0706.

Provide an interpretation of the probability value IN CONTEXT.

C. Is there sufficient evidence to halt production? EXPLAIN.

D. If your decision in Part C was incorrect, what type of error is this? EXPLAIN.

Problem #8

A soft drink bottler purchases glass bottles from a vendor. The bottles are required to have in

internal pressure of at least 150 pounds per square inch (psi). A prospective vendor claims that

its production process yields bottles with a mean internal pressure of 157 psi and a standard

deviation of 3 psi. Before entering an agreement, the bottler will obtain a random sample of 40

bottles from the vendor.

A. If the vendor’s claim is true, what is a “typical value” for average pressure of a sample of 40

bottles? SHOW YOUR WORK.

B. According to the vendor’s claim, what is a measure of variability for the average pressure of a

sample of 40 bottles? SHOW YOUR WORK. SHOW YOUR WORK.

C. What is the probability that the sample average is less than 156 psi?

D. The sample that the bottler obtained has an average pressure of 155.7. Are you surprised at

this result? EXPLAIN.

Engineering Statistics Review For Exam Page 3