Exam (elaborations)

KHAN ACADEMY QUESTIONS AND ANSWERS ALREADY PASSED

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khan academy questions and answers already passed

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KHAN ACADEMY QUESTIONS AND
ANSWERS ALREADY PASSED
A warehouse stores thousands of marble slabs of different shapes, sizes, and materials that are

used for construction projects. The manager wants to estimate the average weight of these slabs.

The slabs are arranged in stacks that have about 10 slabs of different varieties. The manager

wants to weigh a random sample of 100 slabs.

Why might the manager choose a cluster random sample instead of a stratified random sample in

this setting? ✔✔Each stack has a variety of slabs, so choosing all of the slabs in some of the

stacks should represent the population fairly well.

*If each stack reflects the variety in the population, then choosing the stacks as clusters is a good

way to get a sample that looks like the population.

It will probably be easier to weigh heavy slabs that are stacked together rather than pulling out

some slabs from different stacks.

*By weighing entire stacks, the manager would only need to retrieve, weigh, and return about

101010 units. By weighing fewer slabs per stack, there are many more steps in the process and it

is more complicated to track where to return the weighed slabs.

A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the

orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers

of the venue want to survey approximately 150 guests at an upcoming concert about their overall

experience. They want to take a stratified random sample of guests based on the venue's zones.

,Which of these strategies will accomplish their intended design? ✔✔Randomly select 50 tickets

from each zone and invite those guests to participate in the survey.

*This is a stratified random sample since it involves selecting some members from all of the

groups (zones).

A large bakery produces cakes in an assembly line. Sergio noticed a potential defect that seems

to be showing in every other cake. He decides that in the next production run, he'll take a random

sample of cakes to get a better idea of how many cakes might have this defect.

Why might Sergio choose a simple random sample instead of a systematic random sample?

✔✔If the defect is in every other cake, a systematic random sample could miss it completely

depending on what Sergio chooses for k.

*Suppose he starts with the 8th cake and k=10. He would pick cakes 8, 18, 28, 38. If the defect is

in every other cake starting with the cake 1, then none of the cakes in Sergio's sample would

have the defect.

At Amira's pizza shop, they open a fresh batch of pizza sauce for every 10th pizza they make.

Amira decides she wants to take a sample of pizzas in a given day and evaluate their overall

quality. Her shop makes approximately 150 pizzas per day, and she doesn't want to sample more

than 10 pizzas for time's sake.

Amira decides to use a systematic random sample where she'll evaluate every kth pizza made

that day.

,Why might Amira choose k=17 instead of k=10? ✔✔Amira will sample more than 10 pizzas if

she uses k=10.

*She doesn't want to sample more than 101010 pizzas, and 150/10= 15.

In terms of pizza sauce freshness, Amira will likely get a more representative sample if she uses

k=17.

A college professor wants to survey a sample of students taking his course. Here are some details

about his course:

-He teaches 5 sections of the course.

-There are 250 total students across those sections.

-There are 50 graduate students and 200200200 undergraduate students taking the course.

-Each section has about 50 students (some graduate and some undergraduate).

The professor wants to take a sample of 30 students for a survey. He suspects that opinions on

the survey may differ the most based on student type (graduate or undergraduate), so he wants to

design his sample to take that into account.

Which of these strategies will accomplish his intended design? ✔✔Randomly select 6 graduate

students and 24 undergraduate students for the survey.

*A stratified sample like this guarantees that each type of student is proportionately represented

in the survey.

, A college professor wants to survey a sample of students taking her large lecture course. There

are about 150 students in the course, and 10 of those students are graduate students. She wants to

take a systematic random sample of approximately 30 students.

Which of these strategies will accomplish her intended design? ✔✔Randomly select one of the

first 5 students to arrive to class, and every 5th student thereafter to take the survey.

*This is a systematic sample since the students arrive in some order, she selects the kth student,

and then selects every kth student thereafter. Also, 150/5= 30 students.

An airline offers a certain flight once per day that usually contains about 250 passengers. The

flight offers seats in first class (most expensive), business class, and economy class (least

expensive). The airline wants to survey 500 passengers of this flight about their overall

satisfaction. The passengers will be selected using a cluster random sample where each flight is a

cluster.

Why might the airline choose a cluster random sample instead of a simple random sample in this

setting? ✔✔A simple random sample might result in a disproportionate number of passengers

from one or more class, but a cluster sample is less likely to suffer this issue.

Contacting all of the passengers on a few flights will probably be more efficient than contacting

passengers spread out across many flights.

A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the

orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers

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Exam (elaborations)

KHAN ACADEMY QUESTIONS AND ANSWERS ALREADY PASSED

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