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I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible:

$$\ln L1 = \ln(100/63) + 63 \ln(1/2) +(100-63)\ln(1-1/2) = -5.92.$$

Regardless of which calculator I send it to, I do not get this answer. What am I doing wrong, I am at a complete loss.

Dog_69
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Someone
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  • The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you. – angryavian Jan 17 '19 at 21:19
  • The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw. – Someone Jan 17 '19 at 21:30

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What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $\frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.

$$\ln L_1 = \ln \left(\binom{100}{63} 2^{-100}\right) = - 100 \ln 2 + \sum_{k=64}^{100} \ln(k) - \sum_{k=1}^{37} ln(k) = -5.92$$

angryavian
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  • Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot.

    Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!

     – Someone Jan 17 '19 at 21:42
  • @DormantPerson I now see the confusion: you mistook $\binom{100}{63}$ for $\left(\frac{100}{63}\right)$. If you are not familiar with this notation, read about the binomial coefficient. – angryavian Jan 17 '19 at 22:00
  • I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format? – Someone Jan 20 '19 at 17:39
  • @Someone Must be a typo then. – angryavian Jan 20 '19 at 17:50