Question

Colton makes the claim to his classmates that less than 50% of newborn babies born this year in his state are boys. To prove this claim, he selects a random sample of 344 birth records in his state from this year. Colton found that 176 of the newborns are boys. What are the null and alternative hypotheses for this hypothesis test

Answer 1

Answer:

Null hypothesis:$p \leq 0.5$  

Alternative hypothesis:$p > 0.5$  

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

Replacing we got:

$z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445$  

Step-by-step explanation:

Information given

n=344 represent the random sample taken

X=176 represent the anumber of boys babies

$\hat p=\frac{176}{344}=0.512$ estimated proportion of boys babies

$p_o=0.5$ is the value that we want to check

z would represent the statistic

$p_v$ represent the p value

Hypotheis to verify

We want to check if the true proportion of boys is less than 50% then the system of hypothesis are .:  

Null hypothesis:$p\leq 0.5$  

Alternative hypothesis:$p > 0.5$  

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

Replacing we got:

$z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445$