Question

Dr. Ylvis 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. Ylvis takes a random sample of 281 adults 18-25 and asks each person to correctly identify the sound of a fox. Out of the sample of 281, 67 of them were correct. 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 three decimal places and report your answer to three decimal places.

Please help I have missed this one twice and need step by step so I cab figure out where I went wrong. Business Analysis 3363

Answer 1

Answer)

Point estimate P = 67/281 = 0.2384341637010 = 0.238

N = 281

Now we need to check the conditions of normality

If n*p and n*(1-p) both are greater than 5 or not

N*p = 67

N*(1-p) = 214

As both are greater than 5

Conditions are met and we can use standard normal z table to estimate the interval

From z table, critical value z for 99% confidence level is 2.58

Margin of error (MOE) = Z*√P*(1-P)/√N

MOE = 0.0655439348562 = 0.066

Lower bound = P - MOE = 0.238-0.066 = 0.172