# How do I calculate the probability of a type I error in this hypothesis test example? The (lower-tai

Discussion in 'P1.T2. Quantitative Methods (20%)' started by Mikael, Apr 15, 2012.

1. ### MikaelNew Member

Sorry to bring a homework question here, but I'm desperate:
How do I calculate the probability of a type I error in this hypothesis test example?

The (lower-tailed) test involves a poll of 500 people, which showed (the N0 hypothesis) that at least 55% of people are in favour of the war in Afghanistan. I wasn't given any information regarding a the results of a poll used to measure against the null hypothesis, as the assignment involves working out things like the critical value and explaining the test procedure etc. Anyway, the numbers for the test are:
n = 500
p = 0.55
r = 275
Level of significance = 5%
I've worked out the critical level to be 256 with a value of 0.0483, but I'm unsure of how to proceed from here. I read somewhere that the probability for a type I error is equal to α (level of significance), which somehow seems too easy. However, the answers to a similar problem on Yahoo Answers suggested something totally different. There the answer seemed to be the sum of all the probabilities of the values for X that lay outside P(<=X<=12Ip=0.5) I drew up a table for comparison in Excel and got the same results. Regarding my example, do I have to calculate the sum of all the probabilities that lie below my critical level of 256? I'm seriously confused, given that there seem to be so many different answers out there - some way beyond me at present, involving sample variance etc. I've included a snippet of my Excel cumulative probability table - just in case. Any help will be much appreciated.

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