Question

a random sample of 870 births included 430 boys. use a 0.10 significance level to test the claim that 51.3% of newborn babies are boys. do the results support the belief that 51.3% of newborn babies are boys?
c. ( h_{0}: p = 0.513 )
( h_{1}: p
eq 0.513 )
d. ( h_{0}: p = 0.513 )
( h_{1}: p < 0.513 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is -1.12
(round to two decimal places as needed.)
identify the p - value for this hypothesis test
the p - value for this hypothesis test is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 430$ (number of boys) and $n=870$ (sample size). So, $\hat{p}=\frac{430}{870}\approx0.494$.

Step2: Calculate the test statistic (already given as $z=- 1.12$)

For a two - tailed test ($H_1:p
eq0.513$), the P - value is $2P(Z <|z|)$
Since $z=-1.12$, we find $P(Z < - 1.12)$ using the standard normal distribution table.
From the standard normal table, $P(Z < - 1.12)=0.1314$

Step3: Calculate the P - value

The P - value $=2\times0.1314 = 0.2628\approx0.263$

Answer:

The P - value for this hypothesis test is $0.263$