SOLUTION: In a random sample of 45 customers at Amy's Diner, 64% had tea with their breakfast. In a random sample of 53 customers at Bob's Diner, 25% had tea with their breakfast. A hy

Question 1188147: In a random sample of 45 customers at Amy's Diner, 64% had tea with their breakfast.
In a random sample of 53 customers at Bob's Diner, 25% had tea with their breakfast.
A hypothesis test is conducted to determine whether the percentage of customers who have tea with their breakfast at Amy's Diner is equal to the percentage of customers who have tea with their breakfast at Bob's Diner.
Find the value of p̄ , the pooled proportion for this hypothesis test. Round your answer to three decimal places.
Answer: p̄ = __ .
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
pooled proportion is the addition of the two fraction numerators divided by the sum of their denominators, not the average percentage. 64% of 45,or 28.80 or 29/45, since we have to have an integer.
For the second one, it has to be 13/53 as the closest value to 25%, since we can't have 13.25 people
The sum of those two fractions is (29+13)/(45+53)=42/98 or 0.429.
Rough check, the average of the two would be 44.5%, and given the sample sizes are similar but not exact, 43% is reasonable, skewed slightly towards the lower value that had the larger sample size.
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