/sci/ - Science & Math

I'm measuring the Rydberg constant in a lab.

The question:

"Compare your results with the accepted value. What is the probability that your results are in agreement with the accepted value? Be quantitative."

My value: 1.0961 E7 m^-1.
My standard deviation: 0.0020 E6 m^-1
Accepted value: 1.0974 E7 m^-1
Reduced chi^2 = 1.39 +/ sqrt(2)

How do I do that? Confidence interval seems to work backwards. If I'm really close to the accepted value, the chance my values agree should be high, but the confidence value is really low?

How do I measure my agreement with the accepted value quantitatively?

Having some difficulty in my astrophysics course.

2) If a relativistic rocket has a proper acceleration alpha that
increases with proper time tau according to:
alpha(tau) = 2/[Cosine(tau)^2 - Sine(tau)^2]
find its motion, r(t), from the point of view of a control tower
for whom the rocket is motionless at r(0) = 0.
(Hint: alpha(tau) here is the derivative with respect to tau of
ln[tan(tau + pi/4)] .)

I've got it down to:

(1-B)/2 = cos[t*(sqrt(1-B^2)+pi/4]^2

B = v/c.

I'm stuck trying to solve for B (Beta). Once I get B, I can figure out r(t).