Stat 241-Exam Two Practice l. One hundred draws are made from a box containing 1

Question

Stat 241-Exam Two Practice l. One hundred draws are made from a box containing 1 2,34,5,6 and the sum of the draws comes out to be 328. Fill in the The expected value for the sum of the draws is356 the observed value is_228 and the chance error isa lane draws is 350/selhe observed value is 2. Consider the box model consisting of 8 tickets numbered: 0, 1, 1, 2, 2, 3,3, 3. Experiment #1 involves recording the outcomes of single draws from the box repeated 1000 Experiment #2 involves recording the outcomes of the sum of 100 draws from the box repeated 1000 times. One histogram below belongs to experiment #1, one belongs to experiment #2, and one is irrelevant to this question. Which is which? Explain your answer value and standard 3. Suppose a fair coin is flipped one million times. Compute the expected error for the percentage of "heads" from these one million flips. Would it be unusual for this scenario to produce more than 51% heads? Ifso, why? If not, why not? 4. A friend of yours who took Stat 241 last year is extremely bored and so begins to flip a coin and record the outcomes on a sheet of paper. When he gets to 1000 flips he muses aloud, "Hmmm. I've only got 479 heads. That's 21 below what I'd expect. But I remember the Law of Averages tells me that I'll get closer and closer to the expected value the more times I flip this thing. I'l bet if I keep going until I make 10,000 flips I'll probably be fewer than 21 heads away from my expected 5,000". Is your friend right? If not, why not? 5. Within a certain city, exactly 50% of the population is women. Consider the following two scenarios: There will be fewer than 200 women in a 500 person simple random sample from this city. a) b) There will be fewer than 400 women in a 1000 person simple random sample from this city Which of these scenarios is more likely? Or are they equally likely? Why? Note: This problem should not require much computation).

Explanation / Answer

Solution:-

5)

p = 0.50

a) There will be fewer than 200 women in a 500 person simple random sample from this city is 0.00000293.

n = 500

x = 200

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 200) = 0.00000293

b) There will be fewer than 400 women in a 1000 person simple random sample from this city is less than 0.000001.

n = 1,000

x = 400

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 400) = less than 0.000001

Scenario (a) is more likely.

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