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

Solution:

i. Expected number (low birth weight) = np

Expected number (low birth weight) = 350*0.101

Expected number (low birth weight) = 35.35

Expected number (not low birth weight) = n*(1 - p)

Expected number (not low birth weight) =350*(1 - 0.101)

Expected number (not low birth weight) = 314.65

b.

Null Hypothesis (Ho): p1 p2

Alternative Hypothesis (Ha): p1 > p2

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
	350	350.000	0.000	0.221
	.22	chi-square
	1	df
	.6383	p-value

Test Statistics

= 0.22

Degrees of freedom, df = n -1 = 2 - 1 = 1

Using megastat output above, the p-value is 0.6383

Since p-value is greater than 0.10 level of significance, we fail to reject Ho.

Hence, we cannot conclude that mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight babies.

c. Null Hypothesis (Ho): p1 p2

Alternative Hypothesis (Ha): p1 > p2

Pooled proportion, p = (x1 + x2)/ (n1 + n2)

Pooled proportion, p = (0.101*350+0.899*350)/(350 + 350)

Pooled proportion, p = 0.5

Test Statistics

Z = ((0.101 - 0.899)- (0))/ 0.5*0.5*(1/350+350)

Z = -0.798/0.0378

Z = -21.11

Hypothesis test for two independent proportions
	p1	p2	pc
	0.101	0.899	0.5	p (as decimal)
	35/350	315/350	350/700	p (as fraction)
	35.35	314.65	350.	X
	350	350	700	n
		-0.798	difference
		0.	hypothesized difference
		0.0378	std. error
		-21.11	z
		0.0000	p-value (one-tailed, upper)

Using megastat output above, the p-value is 0.000

Since p-value is less than 0.10 level of significance, we reject Ho.

Hence, we can conclude that mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight babies.