Question

Antibiotics in Infancy

Exercise 2.19 describes a Canadian longitudinal study that examines whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included 616 children and found that 438 of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than 70% of Canadian children receive antibiotics during the first year of life.
(a) State the null and alternative hypotheses
(b) Calculate the z-statistic.
(c) Find the p-value.
(d) Make a generic conclusion about the null hypothesis, using α = 0.05
(e) Make a conclusion in context.

Answer 1

e)The information from the sample does not give enough information to support that more than 70% of Canadian children receive antibiotics during the first year of life

Explanation:

The proportion we will use for the test is p = 70 %

From a random sample we got

n = 616

x = 438 then p₁ = 438/616 p₁ = 0,71 p₁ = 71 %

Then q₁ = 1 - p₁ q₁ = 1 - 0,71 q₁ = 0,29 q₁ = 29 %

a) Hypothesis test:

Null hypothesis H₀ p₁ = p

Alternative hypothesis Hₐ p₁ > p >70 %

CI = 95 % significance level α = 5 % α = 0,05

z(c) for α = 0,05 from z-table is z(c) = 1,64

b) To calculate z(s) = ( p₁ - p ) / √ p₁*q₁ / n

z(s) = ( 0,71 - 0,70 )/ √ 0,71*0,29/616

z(s) = 0,01 /0,01828

z(s) = 0,547 ≈ 0,55

c) p-value for z(s) is from z-table p-value ≈ 0,7088

d) p-value > 0,05 then we accept H₀ we don´t have enough evidence to reject H₀

e)The information from the sample does not give enough information to support that more than 70% of Canadian children receive antibiotics during the first year of life