In each of the following cases state whether or not the normal approximation to the binomial should be used for a significance test on the population proportion p.

a. n = 10 and h0: p = 0.4.

b. n = 100 and h0: p = 0.6.

c. n = 1000 and h0: p = 0.996.

d. n = 500 and h0: p = 0.3.

The normal approximation to a binomial can be used for a significance test on the population proportion p if np > 15.


a. n = 10 and H0: p = 0.4. => np = 10(0.4) = 4  [can not be used]

b. n = 100 and H0: p = 0.6.  => np = 100(0.6) = 60 [can be used]

c. n = 1000 and H0: p = 0.996.  => np = 1000(0.996) = 996  [can be used]

d. n = 500 and H0: p = 0.3.  => np = 500(0.3) = 150  [can be used0