Question

According to a census​ company,10.1​%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 240 births for which the mother was 35 to 39 years old and found 28 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 0.101​, 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____

(b) Answer the​ obstetrician's question at the α=0.10 level of significance using the​ chi-square goodness-of-fit test. State the null and alternative hypotheses for this test.

Use technology to compute the​ P-value for this test. Use the Tech Help button for further assistance.

​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.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 α=0.10 level of significance.

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 α=0.10 level of significance.

C.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 α=0.10 level of significance.

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 α=0.10 level of significance.

(c)Answer the​ obstetrician's question at the α=0.10 level of significance using a​ z-test for a population proportion. State the null and alternative hypotheses for this test.

Use technology to compute the​ P-value for this test

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

A. 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 α=0.10 level of significance.

B. 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 α=0.10 level of significance.

C. 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 α=0.10 level of significance.

D. 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 α=0.10 level of significance.

Answer 1