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 350 births for which the mother was 35 to 39 years old and found 38 ?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?

B)- Answer the? obstetrician's question at the alpha equals ?=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. -State a conclusion for this test in the context of the? obstetrician's question.

C)-Answer the? obstetrician's question at the alpha equals ?=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.

Answer 1

Result:

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 350 births for which the mother was 35 to 39 years old and found 38 ?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?

expected number = 350*0.101 =35.35

B)- Answer the? obstetrician's question at the alpha equals ?=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. -State a conclusion for this test in the context of the? obstetrician's question.

Ho: all babies born are of low birth weight is 10.1%

Ha: all babies born are of low birth weight is different from 10.1%

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	38	35.350	2.650	0.199
	312	314.650	-2.650	0.022
Total	350	350.000	0.000	0.221
	0.221	chi-square
	1	df
	0.6383	p-value

P value = 0.6383

Since p value = 0.6383 > 0.10 level, Ho is not rejected.

There is no evidence to reject the company’ claim that , 10.1% of all babies born are of low birth weight.

C)-Answer the? obstetrician's question at the alpha equals ?=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.

Ho: P=0.101

Ha: P?0.101

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.101
Level of Significance	0.1
Number of Items of Interest	38
Sample Size	350
Intermediate Calculations
Sample Proportion	0.108571429
Standard Error	0.0161
Z Test Statistic	0.4701
Two-Tail Test
Lower Critical Value	-1.6449
Upper Critical Value	1.6449
p-Value	0.6383
Do not reject the null hypothesis

Since p value = 0.6383 > 0.10 level, Ho is not rejected.

There is no evidence to reject the company’ claim that , 10.1% of all babies born are of low birth weight.