Question 1059711: A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 373 babies were; born, and 203 of them were girls. Use the sample data with a 0.01 significance level to test the claim that with this method, the probability of a baby being a girl is greater than 0.5. Use this information to answer the following questions
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! :
Our H0: x = 0.5, H1: x < 0.5, so we use a 1-tailed test
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The standard error of the sample must be calculated
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p = 203 / 373 = 0.5442
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standard error = square root( (0.5442 * (1 - 0.5442)) / 373 ) = 0.0258
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We know that the sampling distribution of the proportion is normally distributed with a mean of 0.5 and a standard error of 0.0258.
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sample z-value test statistic = (0.5442 - 0.5) / 0.0258 = 1.7132
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At a 1% significance level, the critical value for a one tailed test is found from the table of z-scores to be 2.33.
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Since the test statistic is less than the critical value for the one-tailed test, we accept the null hypothesis.
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