Question

Will, an art student, randomly sampled oil paintings in a museum. He wanted to find out how many oil paintings in the museum contained the color ultramarine blue. The proportion of paintings that were created using the color ultramarine blue was 0.17, with a margin of error of 0.02. Construct a confidence interval for the proportion of oil paintings that contained ultramarine blue.

Answer 1

The confidence interval is
`0.15 < p < 0.19`

Explanation:

From the question we are told that

The sample proportion is
`\^ p = 0.17`

The margin of error is
`E = 0.02`

Generally the confidence interval for the proportion of oil paintings that contained ultramarine blue is mathematically represented as

`\^ p - E < p < \^ p + E`

=>
`0.17 - 0.02 < p < 0.17 + 0.02`

=>
`0.15 < p < 0.19`