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Chapter 8: Q 8.109. (page 342)
A variable has a mean of and a standard deviation of Four observations of this variable have a mean of and a sample standard deviation of . Determine the observed value of the
a. standardized version of .
b. studentized version of .
Part (a)
Part (b)
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Christmas Spending. In a national poll of U.S. adults, conducted November, Gallup asked "Roughly how much money do you think you personally will spend on Christmas gifts this year?". The data provided on the Weiss Stats site are based on the results of the poll.
a. Determine a upper confidence bound for the mean amount spent on Christmas gifts in (Note: The sample mean and sample standard deviation of the data are and , respectively.)
b. Interpret your result in part (a).
c. In , the mean amount spent on Christmas gifts was . Comment on this information in view of your answer to part (b).
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 z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.
The sample data contain no outliers, the variable under consideration is roughly normally distributed, and the sample size is .
Bottlenose Dolphins. The webpage "Bottlenose Dolphin" produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of adult bottlenose dolphins have a mean length of with a standard deviation of Find and interpret a confidence interval for the mean length of all adult bottlenose dolphins.
A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean.
a. If you know the population standard deviation, which procedure would you use?
b. If you do not know the population standard deviation, which procedure would you use?
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