Chapter 9: Hypothesis Testing with One Sample
Q. 9.4
On a state driver's test, about pass the test on the first try. We want to test if more than pass on the first try. Fill in the correct symbol for the null and alternative hypotheses.
a.
b.
Q.95
"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.
Q. 95
"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 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.
Q. 9.5
Suppose the null hypothesis,, is: the blood cultures contain no traces of pathogen.State the Typeand Typeerrors.
Q.96
"Phillip鈥檚 Wish," by Suzanne Osorio
My nephew likes to play
Chasing the girls makes his day.
He asked his mother
If it is okay
To get his ear pierced.
She said, 鈥淣o way!鈥
To poke a hole through your ear,
Is not what I want for you, dear.
He argued his point quite well,
Says even my macho pal, Mel,
Has gotten this done.
It鈥檚 all just for fun.
C鈥檓on please, mom, please, what the hell.
Again Phillip complained to his mother,
Saying half his friends (including their brothers)
Are piercing their ears
And they have no fears
He wants to be like the others.
She said, 鈥淚 think it鈥檚 much less.
We must do a hypothesis test.
And if you are right,
I won鈥檛 put up a fight.
But, if not, then my case will rest.鈥
We proceeded to call fifty guys
To see whose prediction would fly.
Nineteen of the fifty
Said piercing was nifty
And earrings they鈥檇 occasionally buy.
Then there鈥檚 the other thirty-one,
Who said they鈥檇 never have this done.
So now this poem鈥檚 finished.
Will his hopes be diminished,
Or will my nephew have his fun?
Q. 96
"Phillip鈥檚 Wish," by Suzanne Osorio
My nephew likes to play
Chasing the girls makes his day.
He asked his mother
If it is okay
To get his ear pierced.
She said, 鈥淣o way!鈥
To poke a hole through your ear,
Is not what I want for you, dear.
He argued his point quite well,
Says even my macho pal, Mel,
Has gotten this done.
It鈥檚 all just for fun.
C鈥檓on please, mom, please, what the hell.
Again Phillip complained to his mother,
Saying half his friends (including their brothers)
Are piercing their ears
And they have no fears
He wants to be like the others.
She said, 鈥淚 think it鈥檚 much less.
We must do a hypothesis test.
And if you are right,
I won鈥檛 put up a fight.
But, if not, then my case will rest.鈥
We proceeded to call fifty guys
To see whose prediction would fly.
Nineteen of the fifty
Said piercing was nifty
And earrings they鈥檇 occasionally buy.
Then there鈥檚 the other thirty-one,
Who said they鈥檇 never have this done.
So now this poem鈥檚 finished.
Will his hopes be diminished,
Or will my nephew have his fun?
Q. 9.6
Suppose the null hypothesis, , is: a patient is not sick. Which type of error has the greater consequence, Type or Type?
Q.97
"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.
Q. 97
"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 ,
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.
Q. 9.7
"Red tide" is a bloom of poison-producing algae-a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds (micrograms) of toxin per kg of clam meat in any area, clam harvesting is banned there until the bloom is over and levels of toxin in clams subside. Describe both a Type and a Type error in this context, and state which error has the greater consequence.