Question Preliminary data analyses indicate that you can reasonably apply the t-

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Question Preliminary data analyses indicate that you can reasonably apply the t-interval procedure (Procedure) in Exercise.s E Exercise CH8 135E Bottlenose Dolphins. The webpage "Bottlenose Dolphin" produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of 50 adult bottlenose dolphins have a mean length of 12.04 ft with a standard deviation of 1.03 ft. Find and interpret a 90% confidence interval for the mean length of all adult bottlenose dolphins. PROCEDURE One-Mean t-Interval Procedure PurposeTo find a confidence interval for a population mean, Assumptions 1. Simple random sample 2. Normal population or large sample

Explanation / Answer

BOTTLENOSE DOLPHINS:

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    12.04          
t(alpha/2) = critical t for the confidence interval =    1.676550893          
s = sample standard deviation =    1.03          
n = sample size =    50          
df = n - 1 =    49          
Thus,              
Margin of Error E =    0.244213104          
Lower bound =    11.7957869          
Upper bound =    12.2842131          
              
Thus, the confidence interval is              
              
(   11.7957869   ,   12.2842131   ) [ANSWER]

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