In: Statistics and Probability

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.

*Let P _{1} be the proportion of students who have ear
infections at one school,*

*and P _{2} be the proportion of students who have ear
infections at other school.*

**Hypothesis :**

v/s

**Given data :**

X_{1}=21

n_{1}=42

X_{2}=15

n_{2}=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
H_{0}

**P value at 5% los**

P value = 0.5318 > 0.5

Failed to Reject the null hypothesis and result is not significant

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