AnswersVA-Probability and StatisticsScope of Inference

Scope of Inference Answers

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1
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You and your brother always flip a special golden dollar coin to decide who gets to select the music when the two of you are in the car. The coin has come up heads (in your brother’s favor) on 8 of the last 10 flips. Do 10 flips provide convincing evidence that your brother is using an unfair coin to gain an advantage?

A
Yes, the probability of flipping heads with a fair coin is 0.5. He should have gotten heads exactly 5 times.
B
No, there is no way to determine the probability of flipping heads.
C
Maybe, if the coin comes up tails on 8 of the next 10 flips, then he is using a fair coin.
D
No, 10 trials (flips) is not enough evidence to determine if the coin is fair. We would need many, many more flips to determine the true proportion of heads for this coin.
2
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Moving left to right across a row, select numbers at a time and record the proportion of left-handed individuals.

A
5
B
20
C
100
D
1,000
3

What can we conclude from this graph?

A
This coin appears to be fair because it appears that the proportion of heads is approximately 0.5.
B
The probability of obtaining heads cannot be estimated if we observe a regular and predictable pattern over a long series of trials.
C
This coin appears to be unfair because the proportion of heads fluctuates greatly.
D
If the coin is not fair, we would expect to see the long-run proportion of heads to approach a value other than 0.5.
4

Which statement gives the correct interpretation of this probability?

A
Anne’s return flight is delayed exactly 35% of the time.
B
Anne’s return flight will be on time exactly 65% of the time.
C
If we take a very large sample of Anne’s return flights, we expect about 35% of these flights to be delayed.
D
We cannot draw any conclusions regarding Anne’s flight because probability does not allow us to predict future events.
5

A child is drawing cards from a standard deck of cards, one at a time, observing the color, replacing the card, and shuffling. He observes that 7 consecutive outcomes with a black card have occurred and thinks the next one will be red because "red is due to occur.”Is the child’s reasoning correct?

A
Yes, it is unlikely that the child will draw a black card 7 times in a row, so red must be due.
B
No, if a black card is drawn 7 times in a row, the deck must be unfairly weighted toward black.
C
Yes, the child has to begin drawing red cards in order for the probability of red and black to get back to 0.5.
D
No, red and black outcomes are equally likely, so the probability of drawing a black card is the same regardless of the outcomes of the prior draws.
6

Which of the following outcomes of 2 dice rolls would result in a player winning a water bottle? Check all that apply.

A
1, 1
B
1, 5
C
3, 3
D
2, 3
E
4, 6
F
6, 6
G
5, 6
7

Roll the dice 10 times:

A
even = make; odd = miss
B
1 = make; 2–6 = miss
C
1, 2 = make; 3–6 = miss
8

Repeat:

A
1 time
B
10 times
C
100 times
9

The star basketball player at your high school claims to make 50% of his three-point shots. Recently, he missed 7 of his first 10 three-point shots. Is this surprising for this player? Assume that the player is, in fact, able to make 50% of his three-point shots. We need to carry out a simulation to estimate the probability that he would miss 7 or more of his first 10 three-point shots. Here are the results of 100 simulated trials. Which of the following answers the question of interest?

A
The player’s true three-point success rate is actually only 18%, according to this simulation.
B
Based on the 100 simulated trials, there is about an 18% chance of the player missing 7 of his first 10 three-point shots. This probability is not unusually low, so it is not unlikely.
C
Based on the 100 simulated trials, it is more likely that the player would make 5 or 6 out of every 10 three-point shots.
D
In a very long series of trials, this player should make approximately 50% of his shots. He must have been having an off day.
10

Using a random number table, let digits represent left-handed individuals and let digits represent right-handed individuals.

A
0
B
1–9
C
0–1
D
3–10
11

Using a random number table, let digits represent left-handed individuals and let digits represent right-handed individuals.

A
0
B
1–9
C
0–1
D
3–10
12

The top few hits from a search engine claim that approximately 10% of the population in the United States are left-handed. From a random sample of 20 students at your high school, you find that 6 out of 20 are left-handed, which gives you reason to believe that the true parameter is greater than 10%.Using the table of random numbers and starting at row 1, which of the following gives the correct sequence of left- and right-handed individuals for the first trial of the simulation?

A
RRRRR RRLLR RRRRR LRRRL
B
LLLLL LLRRL LLLLL RLLLR
C
LLRRR LLLLL LLLRR LRLRL
D
RRLLL RRRRR RRRLL RRRRR

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