1a. You measure the rotation curve of the nearest galaxy, Andromeda. You fit thr

Question

1a. You measure the rotation curve of the nearest galaxy, Andromeda. You fit three model rotation curves to the data (models A, B and C), and get the following values of the chi-square statistic: Model A: 21.75 Model B: 16.83 Model C: 36.24 Which model do you conclude fits the data best? A: Model A B: Model B C: Model C D: You can't tell which model fits best because you don't know the expected mean of the chi- square probability distribution 1b The best fit model for the rotation curve has a dark matter mass of 10 million solar masses The 68% confidence interval for your dark matter mass estimate corresponds to a range of 8- 14 million solar masses. Your colleague down the hall makes a very different measurement and concludes that the dark matter mass of Andromeda is 13 million solar masses, with a 95% confidence interval of 12.5-13.5 million solar masses. Does your colleague's result prove that yours is incorrect? A No. Your colleague got a different answer with a much smaller confidence interval. You can't compare your result because the confidence intervals do not agree B No. Your colleague's result is within your 68% confidence interval. Your 68% confidence interval is the range you expect to have a 68% chance of including the true value of the dark matter mass. The fact that your colleague's measurement is inside your confidence interval means that it is consistent with your result. C Yes. Your colleague's result is outside your 68% confidence interval. Your 68% confidence interval is the range you expect to have a 68% chance of including the true value of the dark matter mass. The fact that a more accurate measurement is outside your confidence interval means that it is inconsistent with your result. D Yes. Your colleague's confidence interval does not overlap with your best-fit value. Because your colleague's measurement is more accurate, it must be correct.

Explanation / Answer

1.a

we will use the value for which we get the minimum value of chi- square as it will fit the curve more intensely so we will go for option b (16.83)

1.b

Here answer is no. as the 95% interval of collegue result is under the 68% confidence interval of my results so we can say that both results are consistant to each other. Option b is correct.

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