Question

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 21 of 42 at one school and 15 of 35 at the other had this infection. Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other. Find the test statistic.

Answer 1

Let P₁ be the proportion of students who have ear infections at one school,

and P₂ be the proportion of students who have ear infections at other school.

Hypothesis :

v/s

Given data :

X₁=21

n₁=42

X₂=15

n₂=35

Sample proprotions are

Pooled proportions:

Test statistics :

P value :Is the value of the lowets level of singnificance at which we could reject the Null hypothesis H₀

P value at 5% los

P value = 0.5318 > 0.5

Failed to Reject the null hypothesis and result is not significant