Question

Marine scientists categorize signature whistles of bottlenose dolphins by type —type ​a, type​ b, type​ c, etc. In one study of a sample of 185 whistles emitted from bottlenose dolphins in​ captivity, 96 were categorized as type a whistles.

a. Estimate the true proportion of bottlenose dolphin signature whistles that are type a whistles. Use a 99​% confidence interval.The 99​%confidence interval is ​(nothing​,nothing​).

​(Round to the nearest hundredth as​ needed.)

b. Interpret the result. Choose the correct answer below.

A.We are 11​% confident that the true proportion of bottlenose dolphin signature whistles that are type a whistles is in interval found in previous step.

B.We are 99​%confident that the true proportion of bottlenose dolphin signature whistles that are type a whistles is not in interval found in previous step.

C.We are​ 100% confident that the true proportion of bottlenose dolphin signature whistles that are type a whistles is in interval found in previous step.

D.We are 99%confident that the true proportion of bottlenose dolphin signature whistles that are type a whistles is in interval found in previous step.

Answer 1

a) An 99% confidence interval for true proportion of bottlenose dolphin categorize as type of whistles is

Where,

= 1- confidence level in decimal form

=1-0.99=0.01

Where, x : Number of dolphins categorize as types of whistles = 96

n= sample size =185

(Excel syntax =NORMSINV(0.995)

E= 0.094622

Upper Limit =0.42428

Lower Limit =0.61354

The 99% confidence interval is (0.42428, 0.61354)

b . Interpret result.

Answer D. We are 99% confident that the true proportion of bottlenose dolphin signature whistles that are type a whistles is in interval found in previous step.

Because , Interpretation of confidence interval is we (1-)*100 % confidence on  true estimate is lies between lower limit and upper limit.