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). (Use a significance level of 0.05. Use py - PNy) Autism Autism Typical development Total Periconceptional No vitamin prenatal vitamin Vitamin 112 74 186 141 158 299 Total 253 232 485 (a) State appropriate hypotheses to test for a difference in the rates of autism of children of mothers who did use prenatal vitamins during the first three months before pregnancy and the rates of autism of children of mothers who did not use prenatal vitamins during the first three months before pregnancy. O Ho: Py S PNV H: Py > PNV O Ho: Py > PNV Ha: Py S PNV O Ho: Py s PNV HA: Py* PNV O Ho: Py- PNV HA: Py * PNV O Ho: Pv* PNv Ha: Py - PNV (b) Complete the hypothesis test and state an appropriate conclusion. Check the relevant conditions. The sample is vy random and the sample represents less than vv 10% of all mothers of autistic children and mothers of children with a typical development. Therefore whether or not one mother in the sample vv independent of another. The success-failure condition is took prenatal vitamins in the three months before pregnancy is met since the number of successes and failures is greater than v 10. Calculate the test statistic and determine the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) p-value =

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.