Question

A medical researcher says that at least 25% of U.S. adults are smokers. In a random sample of 200 U.S. adults, 24.5% say they are smokers. At a 99% confidence level, is there enough evidence to reject the researcher's claim?

(Please show all work)

a.)

b.)

c.)

d.)

e.)

Answer 1

a)

H0: p >= 0.25

Ha: p < 0.25

b)

Test statistics

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

= ( 0.245 - 0.25) / sqrt ( 0.25 ( 1 - 0.25) / 200 )

= -0.16

c)

p-value = P(Z < z)

= P(Z < -0.16)

= 0.4364

d)

Decision - Since p-value > 0.01 level. Fail to reject H0.

e)

Conclusion = We do not have sufficient evidence to reject the claim.