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?

h₁: p>0.513

b. h₀: p≠0.513
h₁: p = 0.513

c. h₀: p = 0.513
h₁: p≠0.513

d. h₀: p = 0.513
h₁: p<0.513

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 $\hat{p}$

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 $z$

The formula for the test - statistic in a hypothesis test for a proportion is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$. Here, $p = 0.513$, $\hat{p}\approx0.494$, and $n = 870$.
First, calculate the denominator: $\sqrt{\frac{0.513\times(1 - 0.513)}{870}}=\sqrt{\frac{0.513\times0.487}{870}}\approx\sqrt{\frac{0.25}{870}}\approx\sqrt{0.000287}\approx0.017$.
Then, calculate the numerator: $\hat{p}-p=0.494 - 0.513=-0.019$.
So, $z=\frac{-0.019}{0.017}\approx - 1.12$.

Answer:

The test statistic for this hypothesis test is $-1.12$.