PLEASE NO HANDWRITING - ITS HARD TO INTERPET - THANKS For this question, you wil

Question

PLEASE NO HANDWRITING - ITS HARD TO INTERPET - THANKS

For this question, you will use a fair coin to take some samples and analyze them. First, take any fair coin and flip it 14 times. Count the number of heads out of the 14 flips. This is your first sample. Do this 4 more times and count the number of heads out of the 14 flips in each sample. Thus, you should have 5 samples of 14 flips each. The important number is the number of heads in each sample (this can be any whole number between 0 and 14). Then answer the following questions:

A- If each sample involved flipping the coin 7 times (not 14 times), and you did this for a very large number of samples, what would be the expected number of heads, on average, per set of 7 flips?

B-) On a series of 17 flips of a fair coin, what is the probability of getting 3 or fewer heads OR 14 or more heads?

C-) (Note: The number of coin flips in this sub-question is 20.) If I give you a coin to flip and I tell you it is not a fair coin, but is weighted to come up heads on average only 25% of the time (instead of 50%), what is the most likely number of heads you would observe in a series of 20 flips? If the coin was truly weighted to come up heads on average only 25% of the time, what is the probability that you would observe 9 or more heads in a series of 20 flips? What is the probability that you would observe 3 or fewer heads in a series of 20 flips?

D-) In general, what proportion of samples of fair coin flips (when N is sufficiently large that a rejection region of the binomial distribution exists) should result in rejecting the null hypothesis ( = .05, two-tailed)?

Explanation / Answer

a)if u toss a coin for 7 times

the problility of getting head is 7(1/2)

so answer is 7/2

the problity of avg number of heads

7/4

b)the probility of getteing 3 or 14 is

14(3/2)+14(14/2)

21+98=119

c)20(1/2)

10

for 9 heads

20(9/2)

90

20(3/2)

30

d) nc2^n

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