The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of $p> 0.5$, which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5 . If you have an interest in establishing the success of the method, which of the following P-values would you prefer: $0.999,0.5,0.95,0.05,0.01,0.001$ ? Why?
The P-value of is preferred because it corresponds to the sample evidence that most strongly supports the hypothesis that the method effective
Answer
The preferred P-value would be \(\boxed{0.001}\) because it provides the strongest evidence against the null hypothesis and in favor of the alternative hypothesis, which is that the method increases the likelihood of having a girl.
Step 1 ：The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of \(p>0.5\), which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5 . If you have an interest in establishing the success of the method, which of the following P-values would you prefer: \(0.999,0.5,0.95,0.05,0.01,0.001\) ? Why?
Step 2 ：The P-value is a measure of the probability that an observed difference could have occurred just by random chance. The smaller the P-value, the greater the statistical evidence you have to reject the null hypothesis. In this case, the null hypothesis is that the proportion of girls is not greater than 0.5, and the alternative hypothesis is that the proportion of girls is greater than 0.5.
Step 3 ：Therefore, if we want to establish the success of the method, we would prefer a smaller P-value because it provides stronger evidence against the null hypothesis and in favor of the alternative hypothesis.
Step 4 ：The preferred P-value would be \(\boxed{0.001}\) because it provides the strongest evidence against the null hypothesis and in favor of the alternative hypothesis, which is that the method increases the likelihood of having a girl.
