Engineering Statistics Review For Exam (Page 2 of 4) in pdf

Engineering Statistics Review For Exam Page 2

Problem #3

The caffeine counts (in mg) are given below for a dozen cans of King of Caffeine cola randomly

selected from the production line.

34.2 33.7 31.9 34.3 31.2 32.7

33.1 35.2 31.6 32.9 33.0 32.4

A. Estimate the mean caffeine level among all cans of King of Caffeine cola with 95%

confidence, USING THE APPROPRIATE STEPS.

B. Does your confidence interval support the statement, “A can of King of Caffeine cola

contains less than 30 mg of caffeine, on average.” EXPLAIN.

C. What sample size would be necessary to estimate the mean caffeine level within 0.4 mg with

95% confidence? SHOW YOUR WORK.

Problem #4

The production foreman of Blue Ox Brewing Company claims that the bottling process tends to

overfill. Each bottle of Blue Ox Beer is supposed to contain 12 oz of fluid. A random sample of

40 bottles is taken from bottles coming off the production line, and the contents of each bottle are

carefully measured. It is found that the mean amount of beer for the sample of bottles is 12.1 oz,

and the standard deviation of the sample if 0.2 oz.

A. Does the sample provide sufficient evidence to conclude that, on average, the bottling process

is overfilling? Perform a hypothesis test USING THE APPROPRIATE STEPS.

B. Provide an interpretation IN CONTEXT for your p-value from part A.

C. Describe a Type I error for this problem IN CONTEXT.

D. Describe a Type II error for this problem IN CONTEXT.

Problem #5

According to the Daily Racing Form, there is a 0.67 probability that the favorite in a horse race

will finish "in the money" (that is, first, second or third). Consider a random sample of 200 horse

races.

A. What proportion of the 200 races do you expect the favorite to finish in the money? SHOW

YOUR WORK.

B. Compute a measure of variability for the proportion of races in which the favorite finishes in

the money. SHOW YOUR WORK.

C. Does the proportion of races in which the favorite will finish “in the money” follow a normal

distribution? SHOW YOUR WORK.

D. What is the probability that proportion of races in which the favorite will finish “in the

money” is more than 0.70? SHOW YOUR WORK.

Engineering Statistics Review For Exam Page 2