1."Type I Error Blues," by David Stein

The managers huddled to see if they had won or lost.

Did the new process from 2 months before yield data showing a reduction in cost?

Or was it merely a matter of chance...

Too soon to do the data dance?

So they set about the business of crafting a hypothesis test

In order to conclude which process was best.

With the null hypothesis meaning "status quo", no change evident

They quickly concluded H₀ could not stand, as was their true intent.

Just one month later, they realized their grave mistake!

A Type II error would have been so much safer, for goodness sake.

Alas, their final huddle was a sad one with HR Director Bob.

He told them to go back to training school as each was now in need of a new job.

a.What was the likely managerial mood and outcome on the days immediately following the (erroneous) conclusion to reject this null hypothesis?

b.What would have been the likely managerial mood and outcome on the days immediately following an (erroneous) conclusion not to reject the null hypothesis?

c.In the presence of a Type II Error, what do you suppose would have happened to their cost reduction/process improvement efforts 3-6 months down the road?Please explain in everyday English.

2. "Dalmatian Darnation," by Kathy Sparling

A greedy dog breeder named Spreckles ,Bred puppies with numerous freckles

The Dalmatians he sought, Possessed spot upon spot

The more spots, he thought, the more shekels.

His competitors did not agree, That freckles would increase the fee.

They said, "Spots are quite nice, But they don't affect price;

One should breed for improved pedigree."

The breeders decided to prove, This strategy was a wrong move.

Breeding only for spots, Would wreak havoc, they thought.

His theory they want to disprove.

They proposed a contest to Spreckles, Comparing dog prices to freckles.

In records they looked up, One hundred one pups:

Dalmatians that fetched the most shekels.

They asked Mr. Spreckles to name, An average spot count he'd claim

To bring in big bucks.Said Spreckles, "Well, shucks,

It's for one hundred one that I aim."

Said an amateur statistician, Who wanted to help with this mission.

"Twenty-one for the sample, Standard deviation's ample:

They examined one hundred and one, Dalmatians that fetched a good sum.

They counted each spot,Mark, freckle and dot

And tallied up every one.

Instead of one hundred one spots, They averaged ninety six dots

Can they muzzle Spreckles', Obsession with freckles

Based on all the dog data they've got?

(HINT: The mean of the sample is 96 spots, standard deviation of the sample is 21 spots, n = 101, claim = 101 spots)

a.Define the null hypothesis, H₀

b.Define the alternate (a.k.a. "Researcher's" hypothesis), H

c.In this case, what is the random variable (X_bar) we are testing?

d.Shall we use a t or z test statistic for this situation...and why?

e.What is the test statistic in this case?How exactly is it computed?

f.What is the approximate p-value associated with this test statistic?

g.At a 95% level of confidence...

-What value of alpha (the "critical" value) would we use for this test?

-What is the conclusion of this test?Meaning, do we decide to reject H₀ (or not)?

-What is the reasoning behind this conclusion?

-In everyday English, what do we tell the breeders about the results of this test?

-The breeder asks us to provide our estimate of the true population parameter (in this case, the average number of spots for expensive Dalamations).What would be the 95% confidence interval used for this purpose?How about the 99% CI?

3. "The Craven," by Mark Salangsang

Once upon a morning dreary, In stats class I was weak and weary.

Pondering over last night's homework, Whose answers were now on the board

This I did and nothing more.

While I nodded nearly napping, Suddenly, there came a tapping.

As someone gently rapping,Rapping my head as I snore.

Quoth the teacher, "Sleep no more."

"In every class you fall asleep,"The teacher said, his voice was deep.

"So a tally I've begun to keep, Of every class you nap and snore.

The percentage being forty-four."

"My dear teacher I must confess,While sleeping is what I do best.

The percentage, I think, must be less,A percentage less than forty-four."

This I said and nothing more.

"We'll see," he said and walked away,And fifty classes from that day

He counted till the month of May, The classes in which I napped and snored.

The number he found was twenty-four.

At a significance level of 0.05,Please tell me am I still alive?

Or did my grade just take a dive, Plunging down beneath the floor?

Upon thee I hereby implore.

(HINT: This is a test of proportion with sample proportion being 24/50 and the claimed proportion for population being 0.44)

a.If P' is the proportion of classes in which the student actually falls asleep, define H₀ and H.

b.Shall we use a t or z test statistic for this situation...and why?

c.What is the test statistic in this case?How exactly is it computed?

d.What is the approximate p-value associated with this test statistic?

e.At a 90% level of confidence...

-What value of alpha (the "critical" value) would we use for this test?

-What is the conclusion of this test?Meaning, do we decide to reject H₀ (or not)?

-What is the reasoning behind this conclusion?

-In everyday English, what do we tell the student about the results of this test?