Scatterplot of All Data c. The actual Roman Republic population at the time of C

Question

Scatterplot of All Data c. The actual Roman Republic population at the time of Christ is represented in this scatterplot. What historical explanation is there for this data? Which points would you consider to be outliers? 4,000,000- 3,000,000- 2,000,000- 1,000,000- 0- -500-400-300-200-100 0 Year (B.C.) Classify each probability statement as based on equally likely outcomes, a long-run set observed outcomes, or a subjective assessment: a. Tickets for the Polar Express excursion in Branson sold out for first week of December a. The train's operator announces to shareholders the probability of selling out the second week is 1.0 b. Seating on the train is randomly selected by a computer. There are four seats per row and the window seats on the right side of the train are highly sought after for their view. The probability of getting a right-side window seat is 0.25 Hot chocolate served on the train has real cocoa, a known staining agent for cotton fabrics. While being served hot chocolate, the server accidentally spills some on Janel's cotton sweater. She states to her family that the sweater is ruined, implying a probability of less than 0.10 that the stain can be removed. c. Investigators in a clinical trial use a random number generator to determine which treatment group each subject will be assigned to; in particular, there is a certain probability of being placed in the placebo group. a. Which of these is it: 0.25, 2.5, or 25? b. Was the probability based on equally likely outcomes, a long-run set of observed outcomes, or subjective assessment?

Explanation / Answer

1. An outlier is an observation that is far away from other values in a random sample from a population. From the scatter plot, an outlier is an observation which lies far away in the Y-axis.

Thus from the given diagram the last two points which lie away from all the other points are considered as outliers. These are the points above 4000000.

2. a. It is an example of probability based on long run set of observed outcomes because based on the ticket sold on the first week of december the train's operators predicts the probability of tickets to be sold on the second week

b. It is an example of probability of equally likely outcomes as the probability of getting a seat [window or not] is equal even if the window seat has preference.

c. It is an example of probability based on subjective assessment because here Janel's is stating the probability subjectively.

3.a. Here the probability of getting selected in the group will be 0.25 as probability lies between 0 and 1.

b. Also the probability of getting selected in the group is based on equally likely outcomes as the probabilities of getting selected are equal for every individual.

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