Marine scientists categorize signature whistles of bottlenose dolphins by type—t

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, 95 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.

b. Interpret the result. Choose the correct answer below

A. We are 99% confident that the truth portion of the bottlenose dolphin signature whistles that are type a whistles is not in interval found in previous step

B. We are 1% confident that the true proportion of bottlenose dolphin signature whistles that are type a whistles is in interval found in previous step.

C. 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

D. 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

Explanation / Answer

Ans:

a)sample proportion=95/185=0.514

z value for 99% confidence interval is 2.58

99% confidence interval for true proportion

=0.514+/-2.58*sqrt(0.514*(1-0.514)/185)

=0.514+/-2.58*0.0367

=0.514+/-0.095

=(0.419,0.609)

b)Option C is correct.

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

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