I have established the following hypothesis:
The probability of successfully passing the course in this trial is less than 50% (alternative hypothesis)
The probability of failing the course in this trial is greater than or equal 50% (null hypothesis)
and perform a binomial test in R like the following:
binom.test(10,30,p=0.5)
which means that from 30 students only 10 pass the course, so I am making the hypothesis than 50% of the students will pass the course. I got the following results:
Exact binomial test
data: 10 and 30
number of successes = 10, number of trials = 30, p-value = 0.09874
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
0.1728742 0.5281200
sample estimates:
probability of success
0.3333333
How can I interpret these results? does it mean that I fail to reject the null hypothesis so that I do not have enough evidence that more of half of the class would fail the course?
Update: So should I apply?
binom.test(20,30,.5,alternative="less")
Exact binomial test
data: 20 and 30
number of successes = 20, number of trials = 30, p-value = 0.9786
alternative hypothesis: true probability of success is less than 0.5
95 percent confidence interval:
0.0000000 0.8066916
sample estimates:
probability of success
0.6666667
So I failed to reject the null hypothesis, that means that there is not enough evidence that more of half of the class will fail the course?