Question

Does second-hand 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 1200 babies whose mothers had extensive exposure to second-hand 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 U.S. that are categorized as "low birth weight." Give the null and alternative hypotheses for this research question.
1. H 0 : p = 0.078
H a : p ≠0.078
2. H 0 : p = 0.078
H a : p > 0.078
3. H 0 : p = 0.104
H a : p ≠0.104
4. H 0 : μ = .078
H a : μ > .078

Answer 1

Option 2) Null hypothesis: p = 0.078 , Alternate hypothesis: p > 0.078

Explanation:

We are given the following in the question:

According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birth weight.

Sample size, n = 1200

p = 7.8% = 0.078

We have to carry a hypothesis test whether national percentage is higher than 7.8% or not.

Thus, we can design the null and the alternate hypothesis

`H_(0): p = 0.078\H_A: p > 0.078`

Thus, the correct answer is:

Option 2) Null hypothesis: p = 0.078 , Alternate hypothesis: p > 0.078