Objective: In this project you will explore confidence intervals in a situation

Question

Objective: In this project you will explore confidence intervals in a situation where the population parameter is actually known. You will see for yourself how repeat confidence intervals behave and you will see why we have to interpret them the way we do. Use Excel to crunch the numbers and provide the printout. I want to see all supporting work no matter what. You will lose credit without supporting work.

Part 1: (a) Consider the procedure of flipping a fair coin a fixed number of times and observing X = the number of heads. Give three reasons why the random variable X qualifies as a Binomial random variable. (b) If we define a success as “getting a head”, then we already know what the expected true population proportion of heads is for a fair coin. p = _________ Remember, we usually do not know the value of this population parameter!!

Explanation / Answer

Answer to part 1:

(a)

The FOUR reasons why X qualifies as a binomial random variable is because:

.

(b)

Since we know there are only two possible outcomes head and tail when we toss a coin, therefore the theoretical probability of head is 1/2 or 0.5

Thus P = 0.5 , in this case, in practical manner if suppse 20 coins are tossed , there may say 12 heads and only 8 tails , but as we increase the number of trials , we reach equal number of heads and tails , thus theretically we would always expect the heads and tails to be equal. That is the reason why we already know the vlaue of expected proportion in this exepriment

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