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(3 points) Your friend has lucky coin You are convinced that the lucky coin is biased towards the tail (has larger probability for tail) . Let p denote the true pro...

Question

(3 points) Your friend has lucky coin You are convinced that the lucky coin is biased towards the tail (has larger probability for tail) . Let p denote the true probability of observing tails on any one fip of the coin_ To investigate p YOu plan to Hlip the coin 100 times Which of the options below contains the appropriate null and alternative hypotheses for this experiment? Ho : p = 0.5 vs Ha : p / 0.5 Ho p > 0.5 vs Ha : p = 0.5 Ho p = 0.5 vs Ha : p < 0.5 Ho : p = 0.5 vs Ha : p > 0.5 N

(3 points) Your friend has lucky coin You are convinced that the lucky coin is biased towards the tail (has larger probability for tail) . Let p denote the true probability of observing tails on any one fip of the coin_ To investigate p YOu plan to Hlip the coin 100 times Which of the options below contains the appropriate null and alternative hypotheses for this experiment? Ho : p = 0.5 vs Ha : p / 0.5 Ho p > 0.5 vs Ha : p = 0.5 Ho p = 0.5 vs Ha : p < 0.5 Ho : p = 0.5 vs Ha : p > 0.5 None of the above



Answers

Coin A is loaded in such a way that $P$ (heads) is 0.6. Coin $B$ is a balanced coin. Both coins are tossed. Find: a. The sample space that represents this experiment; assign a probability measure to each outcome b. $P(\text { both show heads })$ c. $P($ exactly one head shows) d. $P(\text { neither coin shows a head })$ e. $P(\text { both show heads } |$ coin A shows a head) f. $P$ (both show heads| coin B shows a head) g. $P$ (heads on coin A | exactly one head shows)

Okay. Your friend is wrong. And the reason why is because they're saying the experiential probability of heads is 2/3. However, remember, theoretical probability of landing heads is always gonna be 1/2. So theoretical. Experiential probability often do not match up, and you must be aware of that.

Okay, so we know that the null hypothesis h not. It's a T is equal to 0.50 on that. No alternative hypothesis. H A S P is not equal to 0.50 Now we can find the that statistic C which is a proportion p my p over the square root of Q P over and something. The proportion is he could x over m, which is equal to 2 52 over 460 which is sample size to give your 0.547 Okay, So like all these values back into this, this is our proportions are end P and he is the former. Q. Is one bias p. You'll get a Z value off 2.5 Okay, Yeah. Now I have to use that Z value to find a P value which is equal to times. But ability. Let's see, was greater than 2.5 which is equal 0.4 your four Andi. Since the P value is less than the significant level which is 0.5 right, we can therefore rejecting the hypothesis on board concluded that the coin toss does not appear to be fair. So I reject the null hypothesis

12. Consider the experiment of Tulsa in a fair coin three times. For each coin, the possible outcomes, our heads or tails. We have heads or tails as the possible outcomes and we're going to pulse it three times a list. The equally likely events of the sample space for the three Tulsa's. So there's three Tulsa's so we could result in heads, Heads, Heads, heads, heads, tails, heads, tails, heads, heads, tails, tails, tails, heads, heads, tails, heads, tails, tails, tails heads or all three tails. There's eight possibilities B. What is the probability that all three coins come up heads? So the probability of heads heads heads. Well, this happens one out of the eight times. So the probability of all three heads is 1/8 part B. Also says notice that the complement of the event three heads is at least one tail. Use this information to compute the probability that there will be at least one tail. So if you notice, the only time that three heads occur is the beginning situation, there's only one time that all three heads occur. In every other situation, we have at least one tales, so the probability of at least one tells is 7/8. These two events are compliments.

Now I have a coin that I'm tossing three times. First time, second time and third time. Okay, Now I want to write down all the equally likely events. What can be my outcomes? Well, it is possible that all three of them are hits our first to our heads. And the last one is a tale, or this is a possibility, or this is a possibility, or this is a possibility, or this is a possibility. Are all three of the Martel's okay? These would be eight in numbers. These eight? Yes, they are right. 1234567 And this is the last one. Eat night. 12345678 Okay, Now, in part, we want to find the probability that all three of them are heads. I see that I have eight possible outcomes, and there is only one outcome in which I have all three of them as heads. So what is my probability that all three of them are hits? It is going to be won by it. Okay, Now, if I think about the compliment off all three heads, compliment off. This is going to be that At least one of them is a tale, right? And this is what the question is asking us. They want us to use this information to compute the probability that there will be at least one tail. So what will be that probability? It will be the complement of this, which is going to be one minus one by eight. And this is going to become seven by it. So this is my probability that I have at least one tail. And even if you count here, you will find that there are seven cases out off eight in which I have at least one tail. 123456 And this last 177 out of it. This is what we've got here.


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