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Chapter 9: Q. 1 (page 536)
You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. What is the random variable? Describe in words.
The random variable defined here is the mean Internet speed in Megabits per second.
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"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)
"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.
Assume the -value is . What type of test is this? Draw the picture of the p-value.
The mean age of De Anza College students in a previous term was years old. An instructor thinks the mean age for online students is older than She randomly surveysonline students and finds that the sample mean iswith a standard deviation of Conduct a hypothesis test.
"The Problem with Angels," by Cyndy Dowling although this problem is wholly mine, the catalyst came from the magazine, Time. On the magazine cover I did find the realm of angels tickling my mind. Inside, I found to be in angels, Americans do believe.
Then, it was time to rise to the task, ninety-five high school and college students I did ask. Viewing all as one group, random sampling to get the scoop. So, I asked each to be true, "Do you believe in angels?" Tell me, do! Hypothesizing at the start, totally believing in my heart that the proportion who said yes would be equal on this test. Lo and behold, seventy-three did arrive, out of the sample of ninety-five. Now your job has just begun, Solve this problem and have some fun.
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