Need help with solving the below problem. Please show work so I can understand.

Question

Need help with solving the below problem. Please show work so I can understand.

A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this writing, 298 babies were born to parents using the new method, and 244 of them were boys. Use a 0.05 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a boy. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

Which of the following is the hypothesis test to be conducted? (I understand this question)

I don’t understand the question below.

What is the test statistic?

z =

What is the P-value?

Explanation / Answer

Note that without intervention, the probability of conceiving a boy is 0.5.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.5
Ha:   p   >   0.5

As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.818791946      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.028964222      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    11.00640448   [ANSWER, TEST STATISTIC]  
          
As this is a    1   tailed test, then, getting the p value using table/technology,  
          
p =    1.77963*10^-28   [ANSWER, P VALUE. This is very close to 0]

*********************************
As P < 0.05, REJECT THE NULL HYPOTHESIS.      

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