
Hypothesis Testing
The times to failure of certain electronic components in accelerate environment tests are 15, 28, 3, 12, 42, 19, 20, 2, 25, 30, 62, 12, 18, 16, 44, 65, 33, 51, 4, and 28 minutes. Looking upon these data as random sample from an exponential population, use the results of:
L = (1/θ^n)*e^[(1/θ)*Σxi]
λ = [( x̅/θ)^n] * e^[((n* x̅ )/θ) + n ]
x̅ * e^( x̅ / θ ) ≤ K, where K = e*θ*k^(1/n)
and use the results of:
For large n, the distribution of 2*ln(λ) approaches, under very general conditions, the chisquare distribution with 1 degree of freedom.
use both of these results to test the null hypothesis θ = 15 minutes against the alternative hypothesis θ ≠ 15 minutes at the 0.05 level of significance. (Use ln(1.763) = 0.570)

Re: Hypothesis Testing
you know the drill by now. Let's see your attempt

Re: Hypothesis Testing
I'm not sure where to start.

Re: Hypothesis Testing
This is what I attempted to do:
n = 20
Σxi = 529
xbar = 26.45
I'm not sure how to solve for theta, but once I have that value, I'd just plug all of that data into the given equations.

Re: Hypothesis Testing
Any hints on how to solve for theta or a push in the right direction would be appreciated.

Re: Hypothesis Testing
I attempted this again:
H_0 : θ = 15
H_1 : θ ≠ 15
alpha = 0.05
Σxi = 529
n = 20
xbar = 26.45
Then I just said to Reject H_0 if x is greater than or equal to 17.
So, P[ x ≥ 17  H_0: θ = 15] = the integral from 17 to infinity of (1/15)*e^((1/15)*x) dx = 0.3220
I'm not sure if this is correct or if I am going in the right direction for solving this problem

Re: Hypothesis Testing