Chapter 8: Q 8.45 (page 331)
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 sample size while keeping the same confidence level.
Accuracy to estimate the population mean is decreased.
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One-Sided One-Mean z-Intervals. Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for -level confidence bounds for a population mean \(\mu\) :
- Lower confidence bound:
- Upper confidence bound:
Interpret the preceding formulas for lower and upper confidence bounds in words.
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 dives was seconds. Assume the population standard deviation is seconds.
a. Find a confidence interval for the mean duration, of an American-alligator dive.
b. Repeal part (a) at a confidence level.
c. Draw a graph similar to Fig. on page 326 to display both confidence intervals.
d. Which confidence interval yields a more accurate estimate of ? Explain your answer.
Assume that the population standard deviation is known and decide weather use of the -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 is.
Poverty and Dietary Calcium. Refer to Exercise 8.70.
a. Find a confidence interval for .
b. Why is the confidence interval you found in part (a) shorter than the one in Exercise 8.70?
c. Draw a graph similar to that shown in Fig on page 326 to display both confidence intervals.
d. Which confidence interval yields a more accurate estimate of ? Explain your answer.
State True or False. Give Reasons for your answers..
The confidence interval can be obtained if you know only the margin of error.
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