Question

Dr. Shaw is a biologist who specializes in the study of animal sounds. He has found that almost everyone can identify the sounds of dogs, cats, birds, mice, cows, frogs, and elephants. The sound that foxes make, however, he believes is less well known. Dr. Shaw takes a random sample of 203 adults between the ages of 18−35 and asks each person to correctly identify the sound of a fox. Out of the sample of 203, 66 of them were correct in identifying the sound. Find the lower bound of a 99% confidence interval for the true proportion of adults 18−25 who can correctly identify the sound of a fox. Take all calculations to at least four decimal places and report your answer to three decimal places.

Answer 1

Dr. Shaw is studying the ability of adults to identify fox sounds. Using a sample of 203 adults, with 66 correctly identifying the sound, the lower bound of a 99% confidence interval for the proportion that can identify the sound is 0.289.

Step-by-step explanation:

Dr. Shaw is interested in determining the proportion of adults between the ages of 18−35 who can correctly identify the sound of a fox. To find the lower bound of a 99% confidence interval, we'll use the sample proportion and the z-value for a 99% confidence level. First, we calculate the sample proportion (p-hat) which is the number of adults who correctly identified the sound divided by the total number in the sample:

p-hat = 66 / 203 = 0.3251

The z-value for a 99% confidence level is approximately 2.576. We then use the formula for the confidence interval lower bound:

Lower bound = p-hat - z*(sqrt(p-hat*(1-p-hat)/n))

Plugging in the values we get:

Lower bound = 0.3251 - 2.576*(sqrt(0.3251*(1-0.3251)/203)) = 0.3251 - 0.0358

Lower bound = 0.2893

To three decimal places, the lower bound is 0.289. Therefore, we are 99% confident that the true proportion of adults who can correctly identify the sound of a fox is at least 0.289.