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Chapter 7: Q. 7.29 (page 300)
Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.
Yes, the sample size has an effect on the standard deviation of all possible sample means.
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A variable of a population has mean 渭 and standard deviation. that For a large sample size n, answer the following questions.
a. Identify the distribution of
b. Does your answer to part (a) depend on n being large? Explain your answer.
c. Identify the mean and the standard deviation of
d. Does your answer to part (c) depend on the sample size being large? Why or why not?
The winner of the 2012-2013 National Basketball Association (NBA) championship was the Miami Heat, One possible starting lineup for that team is as follows:
Part (a): Find the population mean height of the five players.
Part (b): For samples of size 2, construct a table similar to Table 7.2 on page 293. Use the letter in parentheses after each player's name to represent each player.
Part (c): Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.
Part (d): For a random sample of size2, what is the chance that the sample mean will equal the population mean?
Part (e): For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be1 inch or less; that is, determine the probability that will be within1 inch of . Interpret your result in terms of percentages.
Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is thousand. Assume a standard deviation of thousand. Do the following tasks for the variable "annual salary" of classroom teachers.
a. Determine the sampling distribution of the sample mean for samples of size Interpret your answer in terms of the distribution of all possible sample mean salaries for samples of classroom teachers.
b. Repeat part (a) for samples of size
c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.
d. What is the probability that the sampling error made in estimating the population means salary of all classroom teachers by the mean salary of a sample of classroom teachers will be at most ?
e. Repeat part (d) for samples of size
7.1 Why is sampling often preferable to conducting a census for the purpose of obtaining information about a population?
A statistic is said to be an unbiased estimator of a parameter if the mean of all its possible values equals the parameter; otherwise, it is said to be a biased estimator. An unbiased estimator yields, on average, the correct value of the parameter, whereas a biased estimator does not.
Part (a): Is the sample mean an unbiased estimator of the population mean? Explain your answer.
Part (b): Is the sample median an unbiased estimator of the population mean? Explain your answer.
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