The genetics and ivf institute conducted a clinical trial of the ysort method designed to increase the probability of conceiving a boy. as this book was being written, 51 babies were born to parents using the ysort method, and 39 of them were boys. 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 boy is greater than 0.5. does the method appear to work?

Null hypothesis:  

Alternative hypothesis:  

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of boys is significantly higher than 0.5.  

Step-by-step explanation:

1) Data given and notation

n=51 represent the random sample taken

X=39 represent the number of boys

estimated proportion of boys

is the value that we want to test

represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that with this method, the probability of a baby being a boy is greater than 0.5.:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided . The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of boys is significantly higher than 0.5.  

x=5.02012883+πn2,1.26305647+πn2, for any integer n

Step-by-step explanation: