Question

**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 |

Vitamin | 143 | 159 | 302 |

Total | 254 | 229 | 483 |

(a) State appropriate hypotheses to test for independence of use of prenatal vitamins during the three months before pregnancy and autism.

Ho: p_{vitamin} = p_{no vitamin}

Ha: p_{vitamin} < p_{no vitamin}

Ho: p_{vitamin} = p_{no vitamin}

Ha: p_{vitamin} ? p_{no vitamin}

Ho: p_{vitamin} = p_{no vitamin}

Ha: p_{vitamin} > p_{no vitamin}

(b) Complete the hypothesis test and state an appropriate
conclusion.

What is the value of the test statistic for this test? *(Please
round to two decimal places)* What is the p-value associated
with this test? *(Please round to four decimal places)* The
result of the hypothesis is:

Since p<? we fail to reject the null hypothesis

Since p ? ? we do not have enough evidence to reject the null hypothesis

Since p ? ? we reject the null hypothesis and accept the alternative

Since p ? ? we accept the null hypothesis

Since p<? we reject the null hypothesis and accept the alternative

Answer #1

a)Null Hypothesis Ho: pvitamin = pno vitamin

Alternative Hypothesis Ha: pvitamin ? pno vitamin

b) Under H0, the expected frequencies are

Obs. Freq | Exp. Freq | |||||

Autism | Typical Dev | Total | Autism | Typical Dev | Total | |

No Vitamin | 113 | 70 | 181 | 95.18 | 85.82 | 181.00 |

Vitamin | 143 | 159 | 302 | 158.82 | 143.18 | 302.00 |

Total | 254 | 229 | 483 | 254 | 229 | 483.00 |

The calculation for test statistic is

Obs. Freq( O ) | Exp. Freq ( E ) | (O-E)^2/E | |

111 | 95.18 | 2.629 | |

70 | 85.82 | 2.916 | |

143 | 158.82 | 1.576 | |

159 | 143.18 | 1.748 | |

Total | 483 | 483 | 8.869 |

The test statistic is

Degrees of freedom = (2-1)*(2-1) = 1

The critical value of Chi square for 1 df at 5% significance level is 3.841

The P-Value is 0.0029

**Since p<? we reject the null hypothesis and accept
the alternative**

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
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...

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
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
116
68
184
Vitamin
147
166...

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...

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
111
65
176
Vitamin
141
159...

It is believed that nearsightedness affects about 8% of all
children. In a random sample of 194 children, 21 are
nearsighted.
(a) Construct hypotheses appropriate for the following question: do
these data provide evidence that the 8% value is inaccurate?
Ho: p = .08
Ha: p ≠ .08
Ho: p = .08
Ha: p > .08
Ho: p = .08
Ha: p < .08
(b) What proportion of children in this sample are
nearsighted?
(round to four decimal places)
(c)...

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