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Chapter 6: Q6.15 (page 260)
A variable is approximately normally distributed. If you draw a histogram of the distribution of the variable, roughly what shape will it have ?
The histogram of a Normal Distribution is Bell Shaped.
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In Exercises 7鈥�10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.
Sampling Distribution of the Sample Standard Deviation For the following, round results to three decimal places.
a. Find the value of the population standard deviation
b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviation s. Then combine values of s that are the same, as in Table 6-3 (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)
c. Find the mean of the sampling distribution of the sample standard deviation. d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard deviation? Why or why not?
Continuous Uniform Distribution. In Exercises 5鈥�8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.
Greater than 3.00 minutes
Unbiased Estimators Data Set 4 鈥淏irths鈥� in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?
Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can the methods of this section be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of getting a digit less than 3?
In Exercises 11鈥�14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in鈥侰oca-Cola鈥俍ero,鈥侱iet鈥侾epsi,鈥侱r鈥侾epper,鈥俛nd鈥侻ellow鈥俌ello鈥俍ero.
Assume鈥倀hat鈥� random samples of size n = 2 are selected with replacement.
Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means.
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