##### Question

In: Statistics and Probability

# Many elementary school students in a school district currently have ear infections. A random sample of...

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.

## Solutions

##### Expert Solution

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

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