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 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
*z*_{α/2}) for a 99% confidence interval?
**Use the value from the table or, if using software, round
to 2 decimal places.**

*z*_{α/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.

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 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....

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...

I have a fair coin and a weighted coin that lands heads 60% of
the time. I grab a coin at random. I flip that coin 5 times and get
heads 4 times and tails once.
What is the probability that the coin I grabbed was the weighted
coin? (answer to 3 decimal places)

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?...

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.

Question 3: You are
given a fair coin. You flip this coin twice; the two flips are
independent. For each heads, you win 3 dollars, whereas for each
tails, you lose 2 dollars. Consider the random variable
X = the amount of money that you
win.
– Use the definition of expected value
to determine E(X).
– Use the linearity of expectation to
determineE(X).
You flip this coin 99 times; these
flips are mutually independent. For each heads, you win...

Suppose you toss a fair coin 10,000 times. Should you expect to
get exactly 5000 heads? Why or why not? What does the law of
large numbers tell you about the results you are likely to get?
Choose the correct answer below.
1)Should you expect to get exactly 5000 heads? Why or why
not?
A)You shouldn't expect to get exactly 5000 heads, because you
cannot predict precisely how many heads will occur.
B.You shouldn't expect to get exactly 5000 heads,...

A coin is tossed 54 times and 39 heads are observed. Would we
infer that this is a fair coin? Use a 97% level confidence interval
to base your inference.
The sample statistic for the proportion of heads is: (3
decimals)
The standard error in this estimate is: (3
decimals)
The correct z* value for a 97% level confidence interval
is: (3 decimals)
The lower limit of the confidence interval is: (3
decimals)
The upper limit of the confidence interval is: (3
decimals)
Based on...

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