Question

Fair Coin? A coin is called fair if it lands on heads 50% of all possible tosses. You flip a game token 100 times and it comes up heads 60 times. You suspect this token may not be fair.

(a) What is the point estimate for the proportion of heads in all flips of this token? Round your answer to 2 decimal places.

(b) Construct the 99% confidence interval for the proportion of heads in all tosses of this token. Round your answers to 3 decimal places.

(c) Are you 99% confident that this token is not fair?

- No, because 0.50 is within the confidence interval limits.

-Yes, because 0.50 is not within the confidence interval
limits.

-Yes, because 0.50 is within the confidence interval limits.

-No, because 0.50 is not within the confidence interval limits.

Answer #1

Fair Coin? A coin is called fair if it
lands on heads 50% of all possible tosses. You flip a game token
100 times and it comes up heads 42 times. You suspect this token
may not be fair.
(a) What is the point estimate for the proportion of heads in
all flips of this token? Round your answer to 2 decimal
places.
(b) What is the critical value of z (denoted
zα/2) for a 99% confidence interval?
Use the...

A coin is called fair if it lands on heads 50% of all possible
tosses. You flip a game token 100 times and it comes up heads 61
times. You suspect this token may not be fair. (a) What is the
point estimate for the proportion of heads in all flips of this
token? Round your answer to 2 decimal places. (b) What is the
critical value of z (denoted zα/2) for a 90% confidence interval?
Use the value from...

Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.39. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.04 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...

You flip a fair coin. If the coin lands heads, you roll a fair
six-sided die 100 times. If the coin lands tails, you roll the die
101 times. Let X be 1 if the coin lands heads and 0 if the coin
lands tails. Let Y be the total number of times that you roll a 6.
Find P (X=1|Y =15) /P (X=0|Y =15) .

Suppose you flip a fair coin until it lands heads up for the
first time. It can be shown (do not try to calculate this) that the
expected value of the number of flips required is 2. Explain (with
a sentence or two) what this expected value means in this
context.

Consider a coin. Suppose you want to learn about the
distribution of flips of the coin that land on Heads but you only
want to flip the coin 20 times.
Suppose you flip a coin 20 times and record the count
and proportion of times it lands on Heads.
Is the proportion of Heads among the 20 flips of the
coin a parameter or a statistic? What symbol is used to denote the
proportion?
Is the proportion of Heads among...

The theoretical probability of a coin landing heads up is
1/2
Does this probability mean that if a coin is flipped two times,
one flip will land heads up? If not, what does it mean?
Choose the correct answer below.
A.
Yes, it means that if a coin was flipped two times, at least
one of the tosses would land heads up.
B.
Yes, it means that if a coin was flipped two times, exactly
one of the tosses would...

You are flipping a fair coin with one side heads, and the other
tails. You flip it 30 times.
a) What probability distribution would the above most closely
resemble?
b) If 8 out of 30 flips were heads, what is the probability of
the next flip coming up heads?
c) What is the probability that out of 30 flips, not more than
15 come up heads?
d) What is the probability that at least 15 out 30 flips are
heads?...

A fair coin is tossed 4 times, what is the probability
that it lands on Heads each time?

Suppose you toss a coin 100 times. Should you expect to get exactly
50 heads? Why or why not?
A. Yes, because the number of tosses is even, so if the coin
is fair, half of the results should be heads.
B. No, because the chance of heads or tails is the same, the
chance of any number of heads is the same.
C. No, there will be small deviations by chance, but if the
coin is fair, the result...

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