Conditions for Inference

Question 1

A teacher wants an interval for the mean nightly sleep of 900 students using 32 volunteers from her first-period class. Name the failed condition.

Accepted Answer

The random condition fails, because volunteers from one class are not a random sample.

Answer

The independence condition fails, because 32 is more than 10 percent of 900.

Answer

The normal condition fails, because any sample smaller than 40 is not allowed.

Answer

The large counts condition fails, because np = 32 is less than 10.

Question 2

A clinic surveys a simple random sample of 80 patients from 600 patients about wait time in minutes and plans an interval for the mean. Name the failed condition.

Accepted Answer

The independence condition fails, because 80 is more than 10 percent of 600.

Answer

The random condition fails, because 80 patients is too many to choose at random.

Answer

The normal condition fails, because a mean can be used only with 100 patients.

Answer

The large counts condition fails, because no success and failure counts are given.

Question 3

A city takes a random sample of 70 homes from 5,000 homes and finds 6 use solar panels and 64 do not. It wants a one-proportion interval. Name the failed condition.

Accepted Answer

The large counts condition fails, because the success count 6 is less than 10.

Answer

The random condition fails, because 70 homes is too small for a random sample.

Answer

The independence condition fails, because 70 is more than 10 percent of 5,000.

Answer

The normal condition fails, because the failure count 64 is greater than 30.

Question 4

A school posts an online poll and uses the first 120 parent responses out of 1,800 parents; 72 favor a new schedule and 48 do not. Name the failed condition.

Accepted Answer

The random condition fails, because the first online responses are not randomly selected.

Answer

The independence condition fails, because 120 is more than 10 percent of 1,800.

Answer

The large counts condition fails, because 72 and 48 are both less than 100.

Answer

The normal condition fails, because proportions never use success and failure counts.

Question 5

A farm randomly samples 120 trees from an orchard of 900 trees; 30 have a fungus and 90 do not. It wants a one-proportion interval. Name the failed condition.

Accepted Answer

The independence condition fails, because 120 is more than 10 percent of 900.

Answer

The random condition fails, because orchard trees cannot be selected randomly.

Answer

The large counts condition fails, because 30 and 90 are not equal counts.

Answer

The normal condition fails, because the sample size is greater than 30.

Question 6

A random sample of 14 delivery times is taken from 2,000 deliveries, and records show delivery times are strongly right-skewed. The company wants a mean interval. Name the failed condition.

Accepted Answer

The normal condition fails, because the sample is small and the population distribution is strongly skewed.

Answer

The random condition fails, because 14 deliveries cannot represent 2,000 deliveries.

Answer

The independence condition fails, because 14 is more than 10 percent of 2,000.

Answer

The large counts condition fails, because np = 14 is less than 10.

Question 7

A coach estimates the mean height of 700 students using all 25 students on one bus route, chosen for convenience. Heights are roughly symmetric. Name the failed condition.

Accepted Answer

The random condition fails, because a convenient bus route is not a random sample.

Answer

The independence condition fails, because 25 is more than 10 percent of 700.

Answer

The normal condition fails, because roughly symmetric heights are never allowed.

Answer

The large counts condition fails, because mean height is measured in centimeters.

Question 8

A warehouse randomly samples 65 boxes from 500 boxes; 40 pass inspection and 25 do not. It wants a one-proportion interval. Name the failed condition.

Accepted Answer

The independence condition fails, because 65 is more than 10 percent of 500.

Answer

The random condition fails, because a random sample must include every box.

Answer

The large counts condition fails, because 40 and 25 are both above 10.

Answer

The normal condition fails, because the population has only 500 boxes.

Question 9

A random sample of 80 jars from 5,000 jars finds 8 with cracked lids and 72 without cracks. For a one-proportion interval, decide the large counts condition.

Accepted Answer

The large counts condition fails, because 8 successes is less than 10.

Answer

The large counts condition is met, because the sample size 80 is greater than 30.

Answer

The large counts condition fails, because 72 failures is greater than 10.

Answer

The large counts condition is met, because 80 is less than 10 percent of 5,000.

Question 10

A random sample of 120 voters from 20,000 voters finds 18 favor a bond measure and 102 do not. For a one-proportion interval, decide the large counts condition.

Accepted Answer

The large counts condition is met, because 18 successes and 102 failures are both at least 10.

Answer

The large counts condition fails, because 18 successes is less than 30.

Answer

The large counts condition is met, because the population has more than 10,000 voters.

Answer

The large counts condition fails, because 120 voters is less than 10 percent of 20,000.

Question 11

A random sample of 50 seedlings from 1,200 seedlings finds 41 sprout and 9 do not. For a one-proportion interval, decide the large counts condition.

Accepted Answer

The large counts condition fails, because 9 failures is less than 10.

Answer

The large counts condition is met, because 41 successes is greater than 10.

Answer

The large counts condition fails, because 50 seedlings is less than 100.

Answer

The large counts condition is met, because 50 is less than 10 percent of 1,200.

Question 12

A random sample of 90 accounts from 4,000 accounts finds 10 late payments and 80 on-time payments. For a one-proportion interval, decide the large counts condition.

Accepted Answer

The large counts condition is met, because 10 successes and 80 failures are both at least 10.

Answer

The large counts condition fails, because 10 successes must be greater than 10.

Answer

The large counts condition is met, because 90 is less than 10 percent of 4,000.

Answer

The large counts condition fails, because 80 failures is too large for a normal model.

Question 13

A random sample of 35 helmets from 900 helmets finds 12 damaged and 23 not damaged. For a one-proportion interval, decide the large counts condition.

Accepted Answer

The large counts condition is met, because 12 successes and 23 failures are both at least 10.

Answer

The large counts condition fails, because 35 helmets is less than 50.

Answer

The large counts condition fails, because 23 failures is more than 10.

Answer

The large counts condition is met, because 35 is less than 10 percent of 900.

Question 14

A simple random sample of 120 library cards is drawn from 4,000 cards. The library wants an interval for the proportion with late fees. Decide the 10 percent condition.

Accepted Answer

The independence condition is met, because 120 is less than 10 percent of 4,000.

Answer

The independence condition fails, because 120 is greater than 10 percent of 4,000.

Answer

The random condition is met, because 120 cards is less than 4,000 cards.

Answer

The large counts condition is met, because the population has 4,000 cards.

Question 15

A factory selects a simple random sample of 75 phones from a shipment of 600 phones. It wants an interval for the proportion with scratches. Decide the 10 percent condition.

Accepted Answer

The independence condition fails, because 75 is more than 10 percent of 600.

Answer

The independence condition is met, because the 75 phones were randomly selected.

Answer

The random condition fails, because 600 phones is not at least 10 times 75.

Answer

The large counts condition fails, because no scratched-phone count is stated.

Question 16

A park samples 210 trees at random from 1,800 trees to estimate the proportion with beetle damage. Decide the 10 percent condition.

Accepted Answer

The independence condition fails, because 210 is more than 10 percent of 1,800.

Answer

The independence condition is met, because 1,800 is more than 10 percent of 210.

Answer

The random condition fails, because tree damage is not assigned randomly.

Answer

The large counts condition is met, because 210 trees is more than 30.

Question 17

A lab chooses a simple random sample of 34 vials from 350 vials to estimate the proportion that are mislabeled. Decide the 10 percent condition.

Accepted Answer

The independence condition is met, because 34 is less than 10 percent of 350.

Answer

The independence condition fails, because 350 is greater than 10 percent of 34.

Answer

The random condition is met, because the sample size is smaller than 50.

Answer

The large counts condition fails, because 34 vials is not at least 100.

Question 18

A town takes a simple random sample of 45 adults from 12,000 adults; 27 support a recycling rule and 18 do not. Are the conditions for a one-proportion interval met?

Accepted Answer

Yes, the sample is random, 45 is under 10 percent of 12,000, and both counts are at least 10.

Answer

No, the sample is random but being under 10 percent makes independence fail.

Answer

No, the counts 27 and 18 both need to be at least 30.

Answer

Yes, because any sample size above 30 automatically meets every condition.

Question 19

A delivery company randomly samples 60 routes from 8,000 routes to estimate mean delivery time. Past data show route times are roughly symmetric. Are the conditions for a mean interval met?

Accepted Answer

Yes, the sample is random, 60 is under 10 percent of 8,000, and the sample size supports normality.

Answer

No, the random condition fails because route times are measured in minutes.

Answer

No, the independence condition fails because 60 is less than 10 percent of 8,000.

Answer

No, the normal condition fails because a mean interval needs success and failure counts.

Question 20

A school randomly samples 90 students from 5,000 students; 15 have a parking pass and 75 do not. Are the conditions for a one-proportion interval met?

Accepted Answer

Yes, the sample is random, 90 is under 10 percent of 5,000, and both counts are at least 10.

Answer

No, the random condition fails because only students with passes can be counted.

Answer

No, the independence condition fails because 90 is less than 10 percent of 5,000.

Answer

No, the large counts condition fails because 15 is less than 30.

Question 21

A bottling plant randomly samples 40 bottles from 1,000 bottles to estimate mean fill volume in milliliters. Fill volumes are roughly symmetric. Are the conditions for a mean interval met?

Accepted Answer

Yes, the sample is random, 40 is under 10 percent of 1,000, and the distribution is roughly symmetric.

Answer

No, the random condition fails because the bottles come from one plant.

Answer

No, the independence condition fails because 40 is less than 10 percent of 1,000.

Answer

No, the normal condition fails because milliliters are continuous measurements.

Question 22

Researchers select 200 commuters by a random number generator from a list of all 30,000 county commuters. Which condition does this fact establish?

Accepted Answer

The random condition, because the selection was made by chance from the full list.

Answer

The independence condition, because 30,000 commuters is a large population.

Answer

The normal condition, because 200 commuters is larger than 30.

Answer

The large counts condition, because both counts will automatically exceed 10.

Question 23

A survey sample has 150 households, and the city population is 50,000 households. Which condition does this fact establish for an interval?

Accepted Answer

The independence condition, because 150 is less than 10 percent of 50,000.

Answer

The random condition, because a large city always gives a random sample.

Answer

The normal condition, because household counts are measured with whole numbers.

Answer

The large counts condition, because 150 households is more than 10.

Question 24

In a sample of 72 apps from a store with 10,000 apps, 28 have privacy labels and 44 do not. Which condition does this count fact establish?

Accepted Answer

The large counts condition, because 28 successes and 44 failures are both at least 10.

Answer

The random condition, because the sample contains two response groups.

Answer

The independence condition, because the population has 10,000 apps.

Answer

The normal condition for a mean, because 72 apps is greater than 30.

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Conditions for Inference

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Board Games: Teacher-led, projected to the class

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Top Corner

Conditions for Inference

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner