(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A sample of 100 women suffer from dysmenorrhea. A new analgesic is

claimed to provide greater relief than a standard one. After using each

analgesic in a crossover experiment, 40 reported greater relief with the

standard analgesic and 60 reported greater relief with the new one.

Analyze these data.

pi denotes the probability that the new one is judged better. It is desired to estimate

pi and test H0: pi =0.5 against Ha: pi =/= 0.5.

Conduct a likelihood-ratio test and construct a likelihood-based

95% confidence interval. Interpret

2. Relevant equations

3. The attempt at a solution

I know that in order to solve for the likelihood-ratio statistic and compare it to chi-square (3.84), I must solve for lambda

attempt 1: without log-likelihood

which gives me 0.003, which is much smaller than 3.84, and thus fail to reject, but this doesn't seem right, as the Wald test and Score test both rejected the null hypothesis.

Also, I have no idea where to start on the confidence interval calculation, and the professor just sent me this

Here is the detail. LRS < chisquare_0.05(1) => -1.96 < sqrt(LRS) < 1.96.

In R, generate a sequence of grid point on pi, and evaluate sqrt(LRS)

at each pi, and find the pi values at which sqrt(LRR) = -+1.96.

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# Homework Help: Probability Problem - Likelihood-Ratio Test

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