Marine scientists categorize signature whistles of bottlenose dolphins by type —
ID: 3183676 • Letter: M
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, 99 were categorized as type a whistles.
A. Estimate the true proportion of bottlenose dolphin signature whistles that are type a whistle. Use a 99% confidence interval.
The 99% confidence interval is (____,____)
(Round to the nearest hundredth as needed.)
B. Interpret the result. Choose the correct answer below.
a. 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.
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 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.
Explanation / Answer
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=99
Sample Size(n)=185
Sample proportion = x/n =0.535
Confidence Interval = [ 0.535 ±Z a/2 ( Sqrt ( 0.535*0.465) /185)]
= [ 0.535 - 2.576* Sqrt(0.001) , 0.535 + 2.58* Sqrt(0.001) ]
= [ 0.441,0.629]
Interpretations:
1) We are 99% sure that the interval [0.441 , 0.629 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the true population proportion
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.
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