Question

a random sample of 828 births included 427 boys. use a 0.01 significance level to test the claim that 50.9% of newborn babies are boys. do the results support the belief that 50.9% of newborn babies are boys? identify the test statistic for this hypothesis test. the test statistic for this hypothesis test is (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.) identify the conclusion for this hypothesis test. a. fail to reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that 50.9% of newborn babies are boys. b. reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that 50.9% of newborn babies are

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 427$ (number of boys) and $n=828$ (sample size). So, $\hat{p}=\frac{427}{828}\approx0.516$.

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 $p = 0.509$ (the claimed proportion).
Substitute the values:

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Step3: Calculate the P - value

Since this is a two - tailed test (because the claim is about a proportion, not a one - sided claim like "greater than" or "less than"), the P - value is $2\times(1 - P(Z<|z|))$.
Using a standard normal table or calculator, for $z = 0.40$, $P(Z < 0.40)=0.6554$.
So the P - value $=2\times(1 - 0.6554)=2\times0.3446 = 0.689$.

Step4: Make a conclusion

Compare the P - value with the significance level $\alpha=0.01$.
Since $P - value=0.689>0.01$, we fail to reject $H_0$.

Answer:

• The test statistic for this hypothesis test is $0.40$.
• The P - value for this hypothesis test is $0.689$.
• A. Fail to reject $H_0$. There is not sufficient evidence to warrant rejection of the claim that $50.9\%$ of newborn babies are boys.