Question

does secondhand smoke increase the risk of a low birthweight? a baby is considered have low birthweight if he/she weighs less than 5.5 pounds at birth. according to the national center of health statistics, about 7.8% of all babies born in the u.s. are categorized as low birthweight. suspecting that the national percentage is higher than 7.8%, researchers randomly select 1,200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy and find that 10.4% of the sampled babies are categorized as low birth weight. let p be the proportion of all babies in the united states who are categorized as low birth weight. what are the appropriate null and alternative hypotheses for this research question? a. (h_0: p = 0.078) (h_a: p
eq0.078) b. (h_0: p = 0.078) (h_a: p>0.078) c. (h_0: p = 0.104) (h_a: p
eq0.104) d. (h_0: mu = 0.078) (h_a: mu>0.078)

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis ($H_0$) is a statement of no - effect or no difference. The alternative hypothesis ($H_a$) is what we suspect to be true. Here, the national percentage of low - birth - weight babies is 7.8% or 0.078. Researchers suspect that the proportion of low - birth - weight babies is higher than the national rate.

Step2: Determine the correct hypotheses

The null hypothesis should assume that the proportion $p$ is equal to the national proportion. The alternative hypothesis should be a one - sided (right - tailed) hypothesis since we are testing if $p$ is greater than the national proportion. So, $H_0:p = 0.078$ and $H_a:p>0.078$.

Answer:

B. $H_0:p = 0.078$, $H_a:p>0.078$