Question
In: Statistics and Probability
In 10,000 tosses of a coin, 5080 heads occurred. Find a 95% confidence interval for the...
In 10,000 tosses of a coin, 5080 heads occurred. Find
a 95%
confidence interval for the true proportion of heads, and then
decide (based upon that
confidence interval) whether the coin is fair or not.
Solutions
orchestra answered 1 year agoRelated Solutions
Find the probability of getting 8 heads in 12 tosses of a coin.
Find the probability of getting 8 heads in 12 tosses of a
coin.
A coin is flipped 100 times, and 42 heads are observed. Find a 99% confidence interval...
A coin is flipped 100 times, and 42 heads are observed. Find a
99% confidence interval of π (the true population proportion of
getting heads) and draw a conclusion based on the collected data.
Hint: Choose the best one.
A) (0.274, 0.536) a 99% confidence interval of π and we
conclude it is a fair coin.
B) (0.293, 0.547) a 99% confidence interval of π and we
conclude it is a fair coin.
C) (0.304, 0.496) a 99% confidence interval...
An experimenter flips a coin 100 times and gets 42 heads. Find the 90% confidence interval...
An experimenter flips a coin 100 times and gets 42 heads. Find
the 90% confidence interval for the probability of flipping a head
with this coin.
(a) Find the exact probability of exactly 55 heads in 100 tosses of a coin. (b)...
(a) Find the exact probability of exactly 55 heads in 100 tosses
of a coin.
(b) Estimate this probability using normal distribution. Compare
your answers.
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
a coin 30 times and gets 16 heads. Suppose that the outcomes of
sean's coin tosses are iid random variable with probability p1 of
getting heads on each toss while Micah’s outcomes are also iid with
a potentially different probability p2 of getting heads.
(1) Calculate the maximum likelihood and method of moments
estimators of p1.
(2) Show that the MLE of p1 is an MVUE for...
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 0.43. 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...
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...
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