The proportion of baby boys born in the United States has historically been 0.508. You choose an SRS of 50 newborn babies and find that 45% are boys. Do ALL calculations to 5 decimal places before rounding.

So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to  FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of newborn boys babies is not significantly lower than 0.508

Step-by-step explanation:

Data given and notation

n=50 represent the random sample taken

estimated proportion of newborn boys babies

is the value that we want to test

represent the significance level

Confidence=95% or 0.95  (asumed)

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

We assume that we want to check if the true proportion is less than 0.508.

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 .

Calculate the statistic  

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

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 assumed is . The next step would be calculate the p value for this test.  

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

So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to  FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of newborn boys babies is not significantly lower than 0.508