## Hypothesis Testing help!

in a national survey it was found that 40% of young people failed a standard fitness test.

a random sample of 30 young people is taken
i) explain why for such randoms amples the mean number of those whole failed fitness test is 12

Ans: 40% of 30 is 12?

ii) find the probability of the mean number occuring exaplin how you would check whether the mean is also teh modal value. no further calculations neeeded

Ans: i did bionomial to see 12 out of the 30 taking 0.4 as the as the sucsesful probability so

0.4^12 x 0.6^18 x 30C12 = 0.147 but have no idae wer to go from there

and
A local health industry wishes to investigate whether or not the proportion of young people in its area who failed teh fitness test is 40%. A random sample of 20 young people contains 12 who failed teh test.

iii) carry out a suitable hypothesis test at the 5% significance level stating hypothesises and conclusions carefully and find teh critical region for teh test.

no idea how to do it.
any help wud be appreciated =/

thank youu