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Chapter 8: Q 8.80 (page 332)

American Alligators. Refer to Exercise 8.78.

a. Determine the margin of error for the 95%confidence interval.

b. Determine the margin of error for the 99%confidence interval.

c. Compare the margins of error found in parts (a) and (b).

d. What principle is being illustrated?

Short Answer

Expert verified

(a) The margin of error for 95%confidence interval is 23.77seconds.

(b) The margin of error for role="math" localid="1652809930152" 99%confidence interval is 31.23seconds.

(c) Margin of error of 95%confidence level is smaller than that of 99%confidence level.

(d) Same sample size and increased confidence level.

Step by step solution

01

Given Information

From previous exercise, 95%confidence level of 渭is (314.23,361.77).

99%confidence level of渭is(306.77,369.23)

02

Margin of Error for 95% Confidence Interval

Margin of error is calculated as:

E=Upperlimit-Lowerlimit2

E=361.77-314.232

E=47.542

E=23.77seconds

03

Margin of Error for 99% Confidence Interval

Margin of Error is given by

Margin of error=Upper limit-Lower limit2

E=369.23-306.772

E=62.462

E=31.23seconds

04

Comparison of the margins of error found above

It is found from above results that confidence interval of 95%has smaller margin of error than that of99%confidence interval.

05

Principle Illustrated

The principle illustrated is:

When sample size is same and confidence level is increased, margin of error increases.

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Most popular questions from this chapter

Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean.

Increasing the confidence level while keeping same sample size.

Medical Marijuana. An issue with legalization of medical marijuana is "diversion," the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. Researchers S. Sautel et al. study the issue of diversion in the article "Medical Marijuana Use Among Adolescents in Substance Abuse Treatment" . The mean number of days that 120adolescents in substance abuse treatment used medical marijuana in the last six months was 102.72. Assume the population standard deviation is 32days.

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b. Repeat part (a) at a 90%confidence level.

c. Draw a graph similar to Fig. 8.6on page 326to display both confidence intervals.

d. Which confidence interval yields a more accurate estimate of渭 ? Explain your answer.

American Alligators. Multi-sensor data loggers were attached to free-ranging American alligators in a study conducted by Y. Watanabe for the article "Behavior of American Alligators Monitored by Multi-Sensor Data Loggers" (Aquatic Biology, Vol. 18 , pp. 1-8). The mean duration for a sample of 68dives was 338.0seconds. Assume the population standard deviation is 100seconds.

a. Find a 95%confidence interval for the mean duration, 渭of an American-alligator dive.

b. Repeal part (a) at a 99%confidence level.

c. Draw a graph similar to Fig. 8.6on page 326 to display both confidence intervals.

d. Which confidence interval yields a more accurate estimate of 渭? Explain your answer.

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The sample data contain outliers, and the sample size is20.

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a. Determine a 95% confidence interval for the mean number of chips per bag for all 18-ounce bags of Chips Ahoy! cookies, and interpret your result in words.

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