Question

Blanche Mikhail studied the use of prenatal care among low-income African American women. She found that only 51% of those women had adequate prenatal care. Let us assume that for a population of similar low-income African- American women, 51% had adequate prenatal care. If 200 women from this population are drawn at random, what is the probability that less than 45% will have received adequate prenatal care?

1. 0.9554
2. 0.6736
3. 0.3264
4. 0.0446

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.45

H_a : p < 0.45

n = 200

= 0.51

P₀ = 0.45

1 - P₀ = 1 - 0.45 = 0.55

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.51 - 0.45 / [(0.45*0.55) / 200 ]

= 1.70

Test statistic = z = 1.70

P(z < 1.70) = 0.9554

P-value = 0.9554

Option a ) is correct.