Question

a random sample of 857 births included 427 boys. use a 0.01 significance level to test the claim that 51.1% of newborn babies are boys. do the results support the belief that 51.1% of newborn babies are boys?

h₁: p < 0.511

b. h₀: p = 0.511
h₁: p > 0.511

c. h₀: p ≠ 0.511
h₁: p = 0.511

d. h₀: p = 0.511
h₁: p ≠ 0.511

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 sample proportion

The sample proportion $\hat{p}=\frac{427}{857}\approx0.498$.

Step2: Calculate test - statistic

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, $p = 0.511$, $n=857$, and $\hat{p}\approx0.498$.
Substitute the values into the formula:

$$
LATEXBLOCK0
$$

Answer:

The test statistic for this hypothesis test is $-0.76$.