Question

Carmela randomly selected 65 stamps from a stamp collection. Eleven of these were commemorative stamps. What is the interval estimate for the proportion of commemorative stamps in the entire collection if the sampling method had a margin of error of ±0.025?

a. (0.085, 0.135)
b. (0.415, 0.465)
c. (0.145, 0.195)
d. (0.035, 0.085)

Answer 1

To estimate the proportion of commemorative stamps in the entire collection, we can use the plus-four method. The interval estimate for the proportion is (0.085, 0.135).

Step-by-step explanation:

To find the interval estimate for the proportion of commemorative stamps in the entire collection, we can use the plus-four method.

First, calculate the sample proportion by dividing the number of commemorative stamps (11) by the total number of stamps in the sample (65).

Next, add 2 to the number of commemorative stamps and add 2 to the total number of stamps in the sample. Then, divide the adjusted number of commemorative stamps by the adjusted total number of stamps to get the upper bound.

Finally, subtract 2 from the number of commemorative stamps and subtract 2 from the total number of stamps in the sample. Then, divide the adjusted number of commemorative stamps by the adjusted total number of stamps to get the lower bound.

The interval estimate for the proportion of commemorative stamps is (0.085, 0.135), so the correct answer is a. (0.085, 0.135).