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The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At =0.01 level, is the student academic group鈥檚 claim correct?

Short Answer

Expert verified

We can conclude that on average, freshman students study for at least2.5hours or150minutes.

Step by step solution

01

Given information

The freshman students study at least2.5hours per day. The mean study time is137minutes with a standard deviation of45minutes.

02

Explanation

State the hypotheses:

The null hypothesis states that on average, freshman students study at least 2.5hours or 150minutes. In symbols:

H0:150

The alternative hypothesis states that on average, freshman students study less than 2.5hours or 150minutes. In symbols:

H0=<150

State the P-value:

P-value=0.0622

State alpha:

a=0.01

Since the null hypothesis is not rejected, we can conclude that on average, freshman students study for at least 2.5hours or150minutes.

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Most popular questions from this chapter

"The Craven," by Mark Salangsang

Once upon a morning dreary

In stats class I was weak and weary.

Pondering over last night鈥檚 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, 鈥淪leep no more.鈥

鈥淚n every class you fall asleep,鈥

The teacher said, his voice was deep.

鈥淪o a tally I鈥檝e begun to keep

Of every class you nap and snore.

The percentage being forty-four.鈥

鈥淢y 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.鈥

This I said and nothing more.

鈥淲e鈥檒l see,鈥 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.

Determine both TypeIand TypeIIerrors for the following scenario:

Assume a null hypothesis,H0, that states the percentage of adults with jobs is at least 88%.

Identify the TypeIand Type IIerrors from these four statements.

a. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88%when that percentage is actually less than 88%

b. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88%when the percentage is actually at least 88%.

c. Reject the null hypothesis that the percentage of adults who have jobs is at least 88%when the percentage is actually at least 88%.

d. Reject the null hypothesis that the percentage of adults who have jobs is at least 88%when that percentage is actually less than 88%.

"Japanese Girls鈥 Names"

by Kumi Furuichi

It used to be very typical for Japanese girls鈥 names to end with 鈥渒o.鈥 (The trend might have started around my

grandmothers鈥 generation and its peak might have been around my mother鈥檚 generation.) 鈥淜o鈥 means 鈥渃hild鈥 in Chinese characters. Parents would name their daughters with 鈥渒o鈥 attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko鈥攈appy child, Yoshiko鈥攁 good child, Yasuko鈥攁 healthy child, and so on.

However, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with 鈥渒o.鈥 More and more, parents seem to have become creative, modernized, and, sometimes, westernized in naming their children.

I have a feeling that, while 70 percent or more of my mother鈥檚 generation would have names with 鈥渒o鈥 at the end,

the proportion has dropped among my peers. I wrote down all my Japanese friends鈥, ex-classmates鈥, co-workers, and

acquaintances鈥 names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has

dropped for this generation.

Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako,

Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko,

Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko,

Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko,

Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko.

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

order of appearance):

鈥 HAMLET, Prince of Denmark and student of Statistics

鈥 POLONIUS, Hamlet鈥檚 tutor

鈥 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鈥檚 recent experience. Horatio is seated at the large table at right stage.)

POLONIUS: My Lord, how cans鈥檛 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鈥檇, 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, 鈥淲hat 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鈥檛 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 鈥榯is 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)

H0:p=0.5,Ha:p0.5

Assume the p-value is 0.2564. What type of test is this? Draw the picture of the p-value.

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