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Chapter 8: Q.2 (page 477)

In words, define the random variables X andX炉.

Short Answer

Expert verified

The sample mean, x炉 is the point estimate for the population mean 渭.

Step by step solution

01

Given Information 

The random variables areXandX炉.

02

Explanation 

The sample mean, x炉is the point estimate for the population mean 渭.

Suppose that X1,X2,鈥�,Xn, is a random sample from a normal distribution with unknown mean 渭, than test statistic

X炉=X1+X2+鈰�+Xnn,

is normally distributed with mean 渭and variance localid="1648836325806" 蟽2/n.

03

Explanation

It is often necessary to construct confidence intervals on a population proportion. For example, suppose that a random sample of size n has been taken from a large (possibly infinite) population and that X(鈮�n) observations in this sample belong to a class of interest. Then

P炉=Xn

is a point estimator of the proportion of the population p that belongs to this class.

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Most popular questions from this chapter

The Ice Chalet offers dozens of different beginning iceskating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.

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