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Chapter 9: Q. 9.3 (page 507)
We want to test if it takes fewer than minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol for the null and alternative hypotheses.
a.
b.
a. Null hypotheses is greater than or equal to.
b. Alternative hypotheses is less than.
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"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.
A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?
"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)
A particular brand of tires claims that its deluxe tire averages at least miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be . A survey of owners of that tire design is conducted. From the tires surveyed, the mean lifespan was miles with a standard deviation of miles. Using alpha =, is the data highly inconsistent with the claim?
According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is Suppose that a survey is conducted to determine this year鈥檚 rate. Nine out of randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still or if it has decreased.
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