# Hypothesis Testing - Newton or Einstein?

After taking measurements on the deflection of stars during the 1919 eclipse in Borneo...

It was found that:

n = 15
Mean = 1.4824 angular units (AU)
SD = 1.349237 AU
SE = .348371 AU

A) Test the hypothesis that Einstein was correct (that the offset was 1.70 angular units as predicted by his theory). If Isaac Newton was correct, the offset would be 0.85 angular units. State your conclusion and your observations about the data.

B) Determine how many observations would be needed to be 90% sure that you would be able to reject each hypothesis if the other one was correct (using the above variability).

I solved A but I'm not quite sure what to do with B. Tried solving for t value given SE and Mean, SE and 1.7, and SE and 1.3(half way between two hypotheses) but none worked and I'm not sure if any of those are appropriate. Also think it might have something to do with power curves, but not really sure about that either.

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It was actually Principe. The eclipse went nowhere near Borneo. – TonyK Feb 3 '11 at 9:51

## 1 Answer

Hint:

You basically have two hypotheses, each has a distribution for the deflection. This distribution depends on the number of observations as well. So, you compute the probability of rejection of one hypothesis under assumption of the other and you impose it to be 90% . This leads to a t-value which you equate to your test statistic to determine the size of the sample. You do this for both cases and take the maximum of the results.

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