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 | 294 |
Total | 247 | 219 | 466 |
Conduct the hypothesis test for the stated null and alternative. Use αα = K and round numeric answers to three decimal places.
H0H0: The variables use of prenatal vitamins during the three months before pregnancy and autism are independent.
HAHA: 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 three decimal places.
Prenatal Vitamin | Autism | Typical Development |
No vitamin | ||
Vitamin |
2. Calculate the test statistic for this hypothesis test. X2X2 =
3. Calculate the degrees of freedom for this hypothesis test.
4. Calculate the p-value for this hypothesis test. p-value =
5. What is your conclusion using αα = 0.1?
A. Reject H0H0
B. Do not reject H0H0
1) Each expected value = Row Total * Column Total/total. Here Total = 466
Expected | |||
Autism | Typical | Total | |
No Vitamin | 91.17 | 80.83 | 172 |
Vitamin | 155.83 | 138.17 | 294 |
Total | 247 | 219 | 466 |
2) The calculation of the test statistic is as below:
Number | Observed | Expected | (O-E) | (O-E)2 | (O-E)2/E |
1 | 109 | 91.17 | 17.83 | 318 | 3.48811449 |
2 | 138 | 155.83 | -17.83 | 318 | 2.04066562 |
3 | 63 | 80.83 | -17.83 | 318 | 3.93408346 |
4 | 156 | 138.17 | 17.83 | 318 | 2.30157264 |
Total | 11.7644362 |
= 11.76
3) The degrees of freedom = (R - 1) * (c - 1) = (2-1) * (2 - 1) = 1 - 1 = 1
4) The p value for = 11.76, df = 1 is p value = 0.0006
5) Since p value (0.0006) is < (0.10), Option A: Reject H0
The Conclusion: There is sufficient evidence at the 10% level of significance to conclude that the variables use of prenatal vitamins during the three months before pregnancy and autism are not independent.
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