# hypothesis testing for this simple problem

I want to know if my system is functional or not base on 30 trials. so what i did is, I have 1 group with 30 trials. the variable for the group is categorical success or fail. for 30 trials, the system has 30 successes.

how to do the hypothesis testing? i feel like im very wrong.

can i say this? using binomial testing. null hypothesis : the probability of success is 1 which means that the system is functional
alternative hypothesis : the probability of success is not 1 which means that the system is not functional

using 5% significance level i can say that the critical value with n=30 is equal to 30*.05=1.5. calculating the number of trials in which the system fails= 0 fails. with these values 1.5 and 0, 0<1.5. therefore i conclude that the null hypothesis is accepted and the alternative hypothesis is rejected.

• If the null hypothesis is that $p_1$ =$p_2$ and the alternative is $p_1$ not equal to $p_2$ you can't reject the null hypothesis. The way to see is to compute the 95% confidence level for each confidence interval and you will find that they over lap perfectly. This would be true for any confidence level. so you cannot reject the null hypothesis. – Michael R. Chernick Jan 21 '17 at 10:56
• so my hypotheses are wrong and my testing is wrong? what is the proper test for this? – paulj Jan 21 '17 at 12:28
• The exact binomial is fine to use. – Michael R. Chernick Jan 21 '17 at 14:54

Under H0, which assumes that in each run probability of success equals the probability of fails. The probability to obtain N successes is $0.5^N$. In your case p-value= $9.3^{-10}$.