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
eq 0.505 )
b. ( h_0: p = 0.505 )
( h_1: p < 0.505 )
c. ( h_0: p
eq 0.505 )
( h_1: p = 0.505 )
d. ( h_0: p = 0.505 )
( h_1: p > 0.505 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is (square)
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is calculated as $\hat{p}=\frac{x}{n}$, 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 $p = 0.505$ (the proportion in the null hypothesis), $\hat{p}\approx0.514$, and $n = 836$.

First, calculate the denominator:
$\sqrt{\frac{0.505\times(1 - 0.505)}{836}}=\sqrt{\frac{0.505\times0.495}{836}}\approx\sqrt{\frac{0.25}{836}}\approx\sqrt{0.0003}\approx0.017$

Then, calculate the numerator: $\hat{p}-p=0.514 - 0.505=0.009$

Now, calculate the test - statistic:
$z=\frac{0.009}{0.017}\approx - 0.53$

Answer:

A. $H_{0}:p = 0.505$, $H_{1}:p
eq0.505$; The test statistic for this hypothesis test is $-0.53$