Question

A gubernatorial candidate wants to analyze how she is performing with different age groups. Her campaign staff surveyed 150 random constituents in the 18–24 age range and 175 constituents in the 65+ age range. Of those constituents, 67 of the people 18–24 years old and 90 of the people 65+ years old said they planned on voting for the candidate for governor. Find the lower bound of the 99% confidence interval for the difference in population proportions of people 18–24 years old who plan to vote for the candidate for governor and people 65+ years old who plan to vote for the candidate for governor. Let the people 18–24 years old be sample 1 and let the people 65+ years old be sample 2. Assume that the samples are independent. Enter your answer as a decimal rounded to three decimal places.

Answer 1

For 18 - 24 age range : n1 = 150 and x1 = 67

For 65+ age range : n2 = 175 and x2 = 90

Using TI-84 calculator we get, 99% confidence interval for the difference in population proportions of people 18–24 years old who plan to vote for the candidate for governor and people 65+ years old who plan to vote for the candidate for governor is,

-0.211 < p₁ - p₂ < 0.075

where, lower bound = -0.211 and upper bound = 0.075