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.

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