Question

According to a census company, 7.1% of all babies born are of low birth weight. An obstetrician wanted to know
whether mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight
babies. She randomly selected 280 births for which the mother was 35 to 39 years old and found 31 low-birth-weight babies.

Complete parts (a) through (c) below.

(a) If the proportion of low-birth-weight babies for mothers in this age group is 0.071, compute the expected
number of low-birth-weight births to 35- to 39-year-old mothers. What is the expected number of births to mothers
35 to 39 years old that are not low birth weight?

The expected number of low-birth-weight births to 35- to 39-year-old mothers is___________

The expected number of births to mothers 35 to 39 years old that are not low birth weight is____________
(Type integers or decimals.)

(b) Answer the obstetrician's question at the α = 0.05 level of significance using the chi-square goodness-of-fit
test. State the null and alternative hypotheses for this test.

H0: (1)________ (2)_________ 0.071
H1: (3)_________ (4)__________ 0.071

Use technology to compute the P-value for this test.
P-value = _______(Round to three decimal places as needed.)

State a conclusion for this test in the context of the obstetrician's question. Choose the correct answer below.

A. Do not reject the null hypothesis. There is sufficient evidence to
conclude that mothers between the ages of 35 and 39 years give birth
to a higher percentage of low-birth-weight babies at the level
of significance α = 0.05

B. Reject the null hypothesis. There is not sufficient evidence to conclude
that mothers between the ages of 35 and 39 years give birth to a
higher percentage of low-birth-weight babies at the level of
significance α = 0.05

C. Reject the null hypothesis. There is sufficient evidence to conclude that
mothers between the ages of 35 and 39 years give birth to a higher
percentage of low-birth-weight babies at the level of
significance α = 0.05

D. Do not reject the null hypothesis. There is not sufficient evidence to
conclude that mothers between the ages of 35 and 39 years give birth
to a higher percentage of low-birth-weight babies at the level
of significance α = 0.05

(c) Answer the obstetrician's question at the level of significance using a z-test for a population
proportion. State the null and alternative hypotheses for this test α = 0.05

H0: (5)____________ (6)___________ 0.071
H1: (7)______________ (8)_____________ 0.071

Use technology to compute the P-value for this test.
P-value =__________ (Round to three decimal places as needed.)

State a conclusion for this test in the context of the obstetrician's question. Choose the correct answer below.


A. Do not reject the null hypothesis. There is not sufficient evidence to
conclude that mothers between the ages of 35 and 39 years give birth
to a higher percentage of low-birth-weight babies at the level
of significance α = 0.05

B. Reject the null hypothesis. There is not sufficient evidence to conclude
that mothers between the ages of 35 and 39 years give birth to a
higher percentage of low-birth-weight babies at the level of
significance α = 0.05

C. Reject the null hypothesis. There is sufficient evidence to conclude that
mothers between the ages of 35 and 39 years give birth to a higher
percentage of low-birth-weight babies at the level of
significance α = 0.05

D. Do not reject the null hypothesis. There is sufficient evidence to
conclude that mothers between the ages of 35 and 39 years give birth
to a higher percentage of low-birth-weight babies at the level of
significance α = 0.05

Answer 1