Question

A medical researcher says that less than 24​% of adults in a certain country are smokers. In a random sample of 200 adults from that​ country, 17.5​% say that they are smokers. At α=0.05​, is there enough evidence to support the​ researcher's claim? Complete parts​ (a) through​ (e) below. (a) Identify the claim and state H0 and HA (b) Find the critical​ value(s) and identify the rejection​ region(s). (c) Find the standardized test statistic z (d) Decide whether to reject or fail to reject the null hypothesis and​ (d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

Answer 1

a)

H0: p = 0.24

Ha: p < 0.24

b)

Critical value at 0.05 level = -1.645

Rejection region = reject H0 if test statistics z < -1.645

c)

Test statistics

z = -p / sqrt( p( 1 - p) / n)

= 0.175 - 0.24 / sqrt( 0.24 * 0.76 / 200)

= -2.15

d)

Since test statistics value falls in rejection region, that is z < -1.645, we have sufficient evidence to reject H0.

e)

We conclude at 0.05 level that we have enough evidence to support the claim that less than 24% of the adults in

a certain country are smokers.