Decide whether the normal sampling distribution can be used. If it can used , test the claim about the population proportion p at the given level of significance α using the given sample statistics.

Claim: p < 0.16; α = 0.01; Sample statistics: = 0.14, n = 22

*Solution*

To use the normal sampling distribution, both np and np must greater than or equal to 5.

Being by calculation np. The claim p< 0.16 implies the hypothesized proportion p = 0.16.

np = 22(0.16)

= 3.52

Next calculate np. First determine the valve of q.

q = 1 –p

= 1 – 0.16

=0.84

Use the value of q to find nq.

nq = 22(0.84)

= 18.48

Since np is less than 5, the normal sampling distribution cannot be used.

Since the normal sampling distribution cannot be used, the test cannot be performed.