Question

**Prenatal vitamins and Autism.** Researchers
studying the link between prenatal vitamin use and autism surveyed
the mothers of a random sample of children aged 24 - 60 months with
autism and conducted another separate random sample for children
with typical development. The table below shows the number of
mothers in each group who did and did not use prenatal vitamins
during the three months before pregnancy.

Prenatal Vitamin | Autism | Typical Development | Total |

No vitamin | 116 | 68 | 184 |

Vitamin | 147 | 166 | 313 |

Total | 263 | 234 | 497 |

Conduct the hypothesis test for the stated null and alternative. Use ?α = K and round numeric answers to four decimal places.

?0H0: The variables use of prenatal vitamins during the three months before pregnancy and autism are independent.

??HA: The variables use of prenatal vitamins during the three months before pregnancy and autism are not independent.

1. Enter the expected values for the hypothesis test in the table below, rounded to four decimal places.

Prenatal Vitamin | Autism | Typical Development |

No vitamin | ||

Vitamin |

2. Calculate the test statistic for this hypothesis test. ?2X2 =

3. Calculate the degrees of freedom for this hypothesis test.

4. Calculate the p-value for this hypothesis test. p-value =

5. Based on the p-value, we have:

**A.** strong evidence

**B.** some evidence

**C.** very strong evidence

**D.** little evidence

**E.** extremely strong evidence

that the null model is not a good fit for our observed data.

Answer #1

The statistical software output for this problem is :

(2) Test statistics is = 12.0239

(3) Degrees of freedom = 1

(4) p-value = 0.0005

(5) very strong evidence

Prenatal vitamins and Autism. Researchers
studying the link between prenatal vitamin use and autism surveyed
the mothers of a random sample of children aged 24 - 60 months with
autism and conducted another separate random sample for children
with typical development. The table below shows the number of
mothers in each group who did and did not use prenatal vitamins
during the three months before pregnancy.
Prenatal Vitamin
Autism
Typical Development
Total
No vitamin
110
65
175
Vitamin
141
158...

Prenatal
vitamins and Autism. Researchers studying the link between
prenatal vitamin use and autism surveyed the mothers of a random
sample of children aged 24 - 60 months with autism and conducted
another separate random sample for children with typical
development. The table below shows the number of mothers in each
group who did and did not use prenatal vitamins during the three
months before pregnancy.
Prenatal Vitamin
Autism
Typical Development
Total
No vitamin
112
66
178
Vitamin
143
161...

Prenatal vitamins and Autism. Researchers
studying the link between prenatal vitamin use and autism surveyed
the mothers of a random sample of children aged 24 - 60 months with
autism and conducted another separate random sample for children
with typical development. The table below shows the number of
mothers in each group who did and did not use prenatal vitamins
during the three months before pregnancy.
Prenatal Vitamin
Autism
Typical Development
Total
No vitamin
112
66
178
Vitamin
143
161...

Prenatal vitamins and Autism. Researchers
studying the link between prenatal vitamin use and autism surveyed
the mothers of a random sample of children aged 24 - 60 months with
autism and conducted another separate random sample for children
with typical development. The table below shows the number of
mothers in each group who did and did not use prenatal vitamins
during the three months before pregnancy.
Prenatal Vitamin
Autism
Typical Development
Total
No vitamin
109
63
172
Vitamin
138
156...

Prenatal
vitamins and Autism. Researchers studying the link between
prenatal vitamin use and autism surveyed the mothers of a random
sample of children aged 24 - 60 months with autism and conducted
another separate random sample for children with typical
development. The table below shows the number of mothers in each
group who did and did not use prenatal vitamins during the three
months before pregnancy.
Prenatal Vitamin
Autism
Typical Development
Total
No vitamin
108
64
172
Vitamin
138
155...

Prenatal vitamins and Autism. Researchers
studying the link between prenatal vitamin use and autism surveyed
the mothers of a random sample of children aged 24 - 60 months with
autism and conducted another separate random sample for children
with typical development. The table below shows the number of
mothers in each group who did and did not use prenatal vitamins
during the three months before pregnancy.
Prenatal Vitamin
Autism
Typical Development
Total
No vitamin
116
67
183
Vitamin
146
165...

6.34 Prenatal vitamins and Autism: Researchers
studying the link between prenatal vitamin use and autism surveyed
the mothers of a random sample of children aged 24 - 60 months with
autism and conducted another separate random sample for children
with typical development. The table below shows the number of
mothers in each group who did and did not use prenatal vitamins
during the three months before pregnancy (periconceptional period).
(Schmidt, 2011)
Autism
Typical Development
Total
No vitamin
111
70
181...

Suppose a cost-benefit study is conducted to measure the impact
of prenatal vitamin usage to improve birth outcomes and long-term
health of children. The costs are incurred during pregnancy, while
the benefits extend over a long timeframe. Suppose further, that
the researchers conclude that prenatal vitamins are cost-effective
using a 2% discount rate. However, most cost-benefit studies use a
discount rate of 3-5%. Explain whether the use of a lower than
typical discount rate makes these results more convincing or...

Exclusive breastfeeding during the first six months of life is
recommended for optimal infant growth and development. Suppose that
you conducted a survey of randomly chosen women from California and
found that 775 out of 5615 new mothers exclusively breast fed their
infants.
a.) Suppose that in 2010, the rate of exclusive breastfeeding
in
California was known to be 18.6%. Based on the 95% CIs calculated,
is there
evidence against the null hypothesis that the underlying rate is
equal to...

Data:
A simple random sample of school children was categorized based
on the level of school and the children’s preference for a mother
working outside the home.
Elementary Middle High
Working School School School
Mothers Children Children Children
Prefer 37 48 89
No Preference 63 52 11
Use the p-value method and a 0.5% significance level to test the
claim that the populations of elementary school children, middle
school children, and high school children exhibit homogeneous
preferences for working mothers....

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