Question

a random sample of 836 births included 430 boys. use a 0.05 significance level to test the claim that 50.5% of newborn babies are boys. do the results support the belief that 50.5% of newborn babies are boys?
identify the null and alternative hypotheses for this test. choose the correct answer below.
a. $h_0: p = 0.505$
$h_1: p
eq0.505$
b. $h_0: p = 0.505$
$h_1: plt0.505$
c. $h_0: p
eq0.505$
$h_1: p = 0.505$
d. $h_0: p = 0.505$
$h_1: pgt0.505$
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is
(round to two decimal places as needed)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is given by $\hat{p}=\frac{x}{n}$, where $x = 430$ (number of boys) and $n=836$ (sample size).
$\hat{p}=\frac{430}{836}\approx0.514$

Step2: Calculate the test - statistic

The formula for the test - statistic $z$ in a hypothesis test for a proportion is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$, where $p = 0.505$ (hypothesized proportion).
Substitute the values:

$$
LATEXBLOCK0
$$

Answer:

The test statistic for this hypothesis test is $0.52$