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"Blowing Bubbles," by Sondra Prull

Studying stats just made me tense,

I had to find some sane defense.

Some light and lifting simple play

To float my math anxiety away.

Blowing bubbles lifts me high

Takes my troubles to the sky.

POIK! They're gone, with all my stress

Bubble therapy is the best.

The label said each time I blew

The average number of bubbles would be at least 22.

I blew and blew and this I found

From64blows, they all are round!

But the number of bubbles in64blows

Varied widely, this I know.

20per blow became the mean

They deviated by 6, and not16.

From counting bubbles, I sure did relax

But now I give to you your task.

Was22a reasonable guess?

Find the answer and pass this test!

Short Answer

Expert verified

The alternate hypothesis states that the mean number of bubbles is at least less than22remains true.

Step by step solution

01

Given information

The average number of bubbles each time is at least22.

Sample size=64

02

Explanation

Hypothesis:

The null hypothesis claims that the mean number of bubbles is at least22

H0:μ≥22Ha:μ<22

The random variable is X¯, the mean number of bubbles.

By using students't-distribution we get,

tn-1=t64-1=t63

The sample mean X¯=20

Calculate the Zvalue,

t=X¯-μs/n·É³ó±ð°ù±ðμ¾±²õ±è´Ç±è³Ü±ô²¹³Ù¾±´Ç²Ô³¾±ð²¹²Ô,²Ô¾±²õ²õ²¹³¾±è±ô±ð²õ¾±³ú±ðz=X¯-μσ/n=20-226/64=-26/8=-20.75=-2.667

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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)

Draw the graph of a two-tailed test.

Assume the null hypothesis states that the mean is at least 18. Is this a left-tailed, right-tailed, or two-tailed test?

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

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