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If the alternative hypothesis has a not equals ( 鈮 ) symbol, you know to use which type of test?

Short Answer

Expert verified

If a alternative view doesn't quite involve the symbol equals (), a two-tailed test is employed if the alternative hypothesis bears the notation ().

Step by step solution

01

Introduction

The sample and population means are compared in a two-tailed test to see if the difference between them is statistically significant. Despite the fact that both the population and the sample are supposed to be normally distributed, their means differ.

02

Explanation

With a two-tailed test, we're looking for an area in the middle of the distribution. Your rejection zone, on the other hand, is on both ends of the tails (where the null hypothesis is rejected).

A two-tailed test is required when the degree of uncertainty cannot be identified on the higher or lower side.

If the alternative hypothesis has a not equals symbol, we do a two-tailed test.

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Most popular questions from this chapter

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.

"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)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on

average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of

49students and obtain a sample mean of 5.1with a sample standard deviation of 1.2Do the data support your claim at the

1%level?

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273randomly selected teen girls living in Massachusetts (between 12and 15years 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. RejectH0: There is sufficient evidence to conclude that more than30%of teen girls smoke to stay thin.

b. Do not rejectH0: 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.

"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.

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