1. One researcher believes a coin is “fair,” the other
believes the coin is biased toward...
1. One researcher believes a coin is “fair,” the other
believes the coin is biased toward heads. The coin is tossed 21
times, yielding 16 heads. Indicate whether or not the first
researcher’s position is supported by the results. Use α =
.05.
2. Design a decision rule to test the hypothesis that a coin
is fair if a sample of 64 tosses of the coin is taken and if a
level of significance of (a) .05 and (b) .01 is used.
3. The mayor claims that blacks account for 30% of all city
employees. A civil rights group disputes this claim, and argues
that the city discriminates against blacks. A random sample of 120
city employees has 19 blacks. Test the mayor’s claim at the .05
level of significance.
Solutions
Expert Solution
The 1
problem is right tailed test. So we have a single critical value
and is positive.
A box contains three fair coins and one biased coin. For the
biased coin, the probability that any flip will result in a head is
1/3. Al draws two coins from the box, flips each of them once,
observes an outcome of one head and one tail and returns the coins
to the box. Bo then draws one coin from the box and flips it. The
result is a tail. Determine the probability that neither Al nor Bo
removed the...
There is a fair coin and a biased coin that flips heads with
probability 1/4.You randomly pick one of the coins and flip it
until you get a heads. Let X be the number of flips you need.
Compute E[X] and Var[X]
A coin has one face
marked with 1 and the other face marked -1. The coin is tossed four
times. Let X be the sum of four numbers and g(X)=X2.
Determine the
Probability Mass Function (PMF) of X and g(X).
Sketch PMF and CDF for
X.
Sketch PMF and CDF for
g(X).
Evaluate E(X) and
Var(X).
Evaluate E(g(X)) and
Var(g(X)).
A biased coin is flipped 20 times in a row. The coin has a
probability 0.75 of showing Heads.
a. What’s the probability that you get exactly 8 Heads?
b. What’s the probability that you get exactly 8 Heads, given
that the first 2 flips show Heads?
c. What’s the probability that you never see the same result
consecutively( never see 2H or 2T in a row)
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...
Shortly after the introduction of a new coin, newspapers
published articles claiming the coin is biased. The stories were
based on reports that someone had spun the coin
150150
times and gotten
8181
headsminus−that's
5454%
heads.
a right parenthesis font size decreased by 1 a)
Use the Normal model to approximate the Binomial to determine
the probability of spinning a fair coin
150150
times and getting at least
8181
heads.
b right parenthesis font size decreased by 1 b)
Do...
A biased coin has probability p = 3/7 of flipping heads. In a
certain game, one flips this coin repeatedly until flipping a total
of four heads.
(a) What is the probability a player finishes in no more than 10
flips?
(b) If five players independently play this game, what is the
probability that exactly two of them finish in no more than ten
flips?
You toss a biased coin with the probability of heads as p. (a)
What is the expected number of tosses required until you obtain two
consecutive heads ? (b) Compute the value in part (a) for p = 1/2
and p = 1/4.
You have 3 coins that look identical, but one is not a fair
coin. The probability the unfair coin show heads when tossed is
3/4, the other two coins are fair and have probability 1/2 of
showing heads when tossed.
You pick one of three coins uniformly at random and toss it n
times, (where n is an arbitrary fixed positive integer).
Let Y be the number of times the coin shows heads. Let X be the
probability the coin...