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Chapter 7: Q. 70 (page 481)

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

Short Answer

Expert verified

The statement made by the student is Yes, correct

Step by step solution

01

Given information 

The student made a statement "The variability of the sampling distribution of the sample mean diminishes as you take more and larger samples from a population."

02

Explanation 

If the sample size is higher than or equal to 30, the sampling distribution of the sample mean will be nearly normal with mean and standard deviation, according to the central limit theorem is 蟽/n.

The standard deviation of the sampling distribution drops as the value of n increases, and the spread of the sampling distribution of the sample mean decreases.

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Most popular questions from this chapter

Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The standard deviation of the sampling distribution will decrease as the sample size increases.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.

c. The sample mean is an unbiased estimator of the population mean.

d. The sampling distribution shows how the sample mean is distributed around the population mean.

e. The sampling distribution shows how the sample is distributed around the sample mean.

Squirrels and their food supply (3.2) Animal species produce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pinecones, a food source that sometimes has very large crops. Researchers collected data on an index of the abundance of pinecones and the average number of offspring per female over 16years.4Computer output from a least-squares 4regression on these data and a residual plot are shown here

a. Is a linear model appropriate for these data? Explain.

b. Give the equation for the least-squares regression line. Define any variables you use.

c. Interpret the values of r2and sin context.

Here are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked with an arrow on each histogram.

Which statistic would provide the best estimate of the parameter? Justify your answer

Bias and variability The figure shows approximate sampling distributions of 4different

statistics intended to estimate the same parameter.




a. Which statistics are unbiased estimators? Justify your answer.

b. Which statistic does the best job of estimating the parameter? Explain your answer.

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.
See all solutions

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