Question

Five years ago, it was found that 10% of pregnant women smoke during their pregnancy. The Gallup organization is interested in testing whether this proportion has decreased today.

a) What would the null and alternative hypothesis for testing whether the proportion of pregnant women who smoke during their pregnancy has decreased from five years ago?

b) Calculate the P-value if a sample of 400 pregnant women were taken today and it was found that 35 of them are smoking during their pregnancy.

c) What conclusion would you make at an alpha level of .05? (State your conclusion in terms of the problem)

Answer 1

a)

H0: p = 0.10

Ha: p < 0.10

b)

Sample proportion = 35 / 400 = 0.0875

Test statistics

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

= ( 0.0875 - 0.10) / sqrt ( 0.10 ( 1 - 0.10) / 400 ]

= -0.83

p-value = P(Z < z)

= P(Z < -0.83) = 0.2033

c)

Since p-value > 0.05 , Fail to reject H0.

We do not have sufficient evidence to support the claim that proportion has decreased.