Chapter 7: Q 3RP. (page 310)
Provide two synonyms for the distribution of all possible sample means for samples of a given size.
1. Sampling distribution of the sample mean.
2. The distribution of the random variable
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Does the sample size have an effect on the mean of all possible sample mean? Explain your answer.
Population data:
Part (a): Find the mean, ,of the variable.
Part (b): For each of the possible sample sizes, construct a table similar to Table on the page and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig on page .
Part (c): Construct a graph similar to Fig and interpret your results.
Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.
Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most .
A variable of a population is normally distribution with mean and standard deviation
a. Identify the distribution of
b. Does your answer to part (a) depend on the sample size? Explain your answer.
c. Identify the mean and the standard deviation of
d. Does your answer to part (c) depend on the assumption that the variable under consideration is normally distributed? Why or why not?
Population data: .
Part (a): Find the mean, , of the variable.
Part (b): For each of the possible sample sizes, construct a table similar to Table on the page and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig on page .
Part (c): Construct a graph similar to Fig and interpret your results.
Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.
Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most .
Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
