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?
d. fail to reject ( h_0 ). there is sufficient evidence to warrant rejection of the claim that 51.3% of newborn babies are boys.
do the results support the belief that 51.3% of newborn babies are boys?
a. the results do not support the belief that 51.3% of newborn babies are boys because there was sufficient evidence to show that the belief is untrue.
b. the results support the belief that 51.3% of newborn babies are boys because there was no evidence to show that the belief is untrue.
c. the results support the belief that 51.3% of newborn babies are boys because there was sufficient evidence to show that the belief is true.
d. the results do not support the belief that 51.3% of newborn babies are boys; the results merely show that there is not strong evidence against the rate of 51.3%.

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{430}{870}\approx0.494$

Step2: State the hypotheses

$H_0:p = 0.513$ (claim), $H_1:p
eq0.513$

Step3: Calculate the test statistic

The formula for the test statistic $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$
Substitute $\hat{p}=0.494$, $p = 0.513$, $n = 870$
$z=\frac{0.494 - 0.513}{\sqrt{\frac{0.513\times(1 - 0.513)}{870}}}\approx\frac{- 0.019}{\sqrt{\frac{0.513\times0.487}{870}}}\approx\frac{-0.019}{\sqrt{\frac{0.250}{870}}}\approx\frac{-0.019}{0.017}\approx - 1.12$

Step4: Find the critical values

For a two - tailed test with $\alpha=0.10$, the critical values are $z=\pm1.645$

Step5: Make a decision

Since $-1.645<-1.12 < 1.645$, we fail to reject $H_0$

Answer:

D. The results do not support the belief that 51.3% of newborn babies are boys; the results merely show that there is not strong evidence against the rate of 51.3%.