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Chapter 8: Q 8.134. (page 343)

Bottlenose Dolphins. The webpage "Bottlenose Dolphin" produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of 50adult bottlenose dolphins have a mean length of 12.04ftwith a standard deviation of 1.03ft Find and interpret a 90% confidence interval for the mean length of all adult bottlenose dolphins.

Short Answer

Expert verified

The 90%confidence interval for μis (11.796,12.284)

Step by step solution

01

Given information

The average length of 50 adult bottlenose dolphins was 12.04ft with a standard deviation of 1.03ft

02

Concept

The formula used: Z=x¯±ta2sn

03

Calculation

Find a90% confidence interval for all adult bottlenose dolphins' mean length.
Consider x¯=12.04,n=50,s=1.03, and the confidence level is 90%

From "Table IV Values of tα" the required value tα2for 90%confidence with 49(=50-1)degrees of freedom is 1.677

The 90%confidence interval is,

x¯±ta2sn=12.04±1.6771.0350=12.04±0.2443=(55-3.3688,55+3.3688)=(11.796,12.284)

As a result, (11.796,12.284) is the 90% confidence interval for μ

The 90%confidence interval for all adult bottlenose dolphins' mean length is between11.796ftand 12.284ft

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Most popular questions from this chapter

State True or False. Give Reasons for your answers.

The margin of error can be determined if you know only the confidence level.

State True or False. Give Reasons for your answers.

The length of the confidence interval can be determined if you know only the margin of error.

Suppose that a simple random sample is taken from a normal population having a standard deviation of 10 for the purpose of obtaining a 95% confidence interval for the mean of the population.

a. If the sample size is 4 , obtain the margin of error.

b. Repeat part (a) for a sample size of 16

c. Can you guess the margin of error for a sample size of 64 ? Explain your reasoning.

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