Question
In: Statistics and Probability
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the
proportion of heads was found to be 0.43. 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 0.03 at the 95% confidence level.
(a) What is the minimum number of tosses required to obtain
this type of accuracy? Use the prior sample proportion in your
calculation.
You should toss the token at least
Incorrect: Your answer is incorrect.
times.
(b) What is the minimum number of tosses required to obtain
this type of accuracy when you assume no prior knowledge of the
sample proportion?
You should toss the token at least
Incorrect: Your answer is incorrect.
times.
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 41 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 value from the table or, if using
software, round to 2 decimal places.
zα/2 =
(c) What is the margin of error (E) for a 99% confidence
interval? Round your answer to 3 decimal places.
E =
(d) Construct the 99% confidence interval for the proportion
of heads in all tosses of this token. Round your answers to 3
decimal places.
< p <
(e) 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.
Solutions
Expert Solution
Solution:-
(a) The minimum number of tosses required to obtain this type of accuracy is 1047.
p = 0.43, M.E = 0.03, n = 100
(b) The minimum number of tosses required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion is 1068.
p = 0.50 (No prior information)
M.E = 0.03, n = 100
orchestra answered 1 year agoRelated Solutions
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.43. 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 0.05 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...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.58. 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 0.05 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...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.58. 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 0.05 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...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the proportion
of heads was found to be 0.61. 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 0.03
at the 95% confidence level. (a) What is the minimum number of
tosses required to obtain this type of accuracy? Use the prior
sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the proportion
of heads was found to be 0.61. 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...
In a series of 100 tosses of a token, the proportion of heads was found to...
In a series of 100 tosses of a token, the proportion of heads
was found to be 0.58. 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 95%
confidence level. (a) What is the minimum number of tosses required
to obtain this type of accuracy? Use the prior sample proportion in
your calculation. You...
Let X be the number of heads in two tosses of a fair coin. Suppose a...
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Toss a fair coin repeatedly. Let N1 be the number of tosses required to obtain heads...
Toss a fair coin repeatedly. Let N1
be the number of tosses required to obtain heads followed
immediately by tails. Let N2 be the number of tosses
required to obtain two heads in a row.
(A) Should N1 and N2
have the same expected value? If not, which expected value should
be larger? Explain your answers.
(B) Find the probability mass function of
N1.
(C) Find the expected value of N1.
(D) Find the probability mass function of
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(E)...
(a) Find the exact probability of exactly 55 heads in 100 tosses of a coin. (b)...
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sean tosses a coin 40 times and gets 15 heads while Micah tosses a coin 30...
sean tosses a coin 40 times and gets 15 heads while Micah tosses
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(1) Calculate the maximum likelihood and method of moments
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