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Draw the graph of a two-tailed test.

Short Answer

Expert verified

The general two-tailed test graph is:

Step by step solution

01

Introduction

In statistics, a two-tailed test is a procedure that uses a two-sided critical area of a distribution to determine if a sample is larger than or less than a certain range of values. It's utilized in statistical significance testing and null hypothesis testing.

02

Explanation

The general graph of a two-tailed test is as follow:

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Most popular questions from this chapter

"William Shakespeare: The Tragedy of Hamlet, Prince of Denmark," by Jacqueline Ghodsi THE CHARACTERS (in

order of appearance):

• HAMLET, Prince of Denmark and student of Statistics

• POLONIUS, Hamlet’s tutor

• HOROTIO, friend to Hamlet and fellow student

Scene: The great library of the castle, in which Hamlet does his lessons

Act I

(The day is fair, but the face of Hamlet is clouded. He paces the large room. His tutor, Polonius, is reprimanding Hamlet

regarding the latter’s recent experience. Horatio is seated at the large table at right stage.)

POLONIUS: My Lord, how cans’t thou admit that thou hast seen a ghost! It is but a figment of your imagination!

HAMLET: I beg to differ; I know of a certainty that five-and-seventy in one hundred of us, condemned to the whips and

scorns of time as we are, have gazed upon a spirit of health, or goblin damn’d, be their intents wicked or charitable.

POLONIUS If thou doest insist upon thy wretched vision then let me invest your time; be true to thy work and speak to

me through the reason of the null and alternate hypotheses. (He turns to Horatio.) Did not Hamlet himself say, “What piece

of work is man, how noble in reason, how infinite in faculties? Then let not this foolishness persist. Go, Horatio, make a

survey of three-and-sixty and discover what the true proportion be. For my part, I will never succumb to this fantasy, but

deem man to be devoid of all reason should thy proposal of at least five-and-seventy in one hundred hold true.

HORATIO (to Hamlet): What should we do, my Lord?

HAMLET: Go to thy purpose, Horatio.

HORATIO: To what end, my Lord?

HAMLET: That you must teach me. But let me conjure you by the rights of our fellowship, by the consonance of our youth,

but the obligation of our ever-preserved love, be even and direct with me, whether I am right or no.

(Horatio exits, followed by Polonius, leaving Hamlet to ponder alone.)

Act II

(The next day, Hamlet awaits anxiously the presence of his friend, Horatio. Polonius enters and places some books upon the

table just a moment before Horatio enters.)

POLONIUS: So, Horatio, what is it thou didst reveal through thy deliberations?

HORATIO: In a random survey, for which purpose thou thyself sent me forth, I did discover that one-and-forty believe

fervently that the spirits of the dead walk with us. Before my God, I might not this believe, without the sensible and true

avouch of mine own eyes.

POLONIUS: Give thine own thoughts no tongue, Horatio. (Polonius turns to Hamlet.) But look to’t I charge you, my Lord.

Come Horatio, let us go together, for this is not our test. (Horatio and Polonius leave together.)

HAMLET: To reject, or not reject, that is the question: whether ‘tis nobler in the mind to suffer the slings and arrows of

outrageous statistics, or to take arms against a sea of data, and, by opposing, end them. (Hamlet resignedly attends to his

task.)

(Curtain falls)

"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?

It’s a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows:

H0:p=0.50,Ha:p>0.50

α=0.01

p-value=0.025.

Interpret the results and state a conclusion in simple, non-technical terms.

You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you

think it is less for this particular coin. What type of test would you use?

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

a. Reject H0: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

b. Do not reject H0: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

c. Do not reject H0: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

d. Reject H0: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

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