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Chapter 10: Q. 10.34 (page 415)

10.34 Explain why sp is called the pooled sample standard deviation.

Short Answer

Expert verified

Let, spaggregates data from both samples' variability into a single estimate of the population standard deviation's common value. As a result, pooled standard deviation is referred to as sp.

Step by step solution

01

Given information

To explain why sp is called the pooled sample standard deviation.

02

Explanation

A test statistic is used when running a hypothesis test based on independent samples to compare the means of two populations with equal and unknown standard deviations.
Individual sample variances of two populations, s12and s22, are taken and pooled by weighting them according to their sample size or degree of freedom, n1and n2, respectively.
sp=n1-1s1+2n2-1s22n1+n2-2
Let, sp aggregates data from both samples' variability into a single estimate of the population standard deviation's common value.
As a result, pooled standard deviation is referred to as sp.

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Most popular questions from this chapter

In each of Exercises 10.75-10.80, we have provided summary statistics for independent simple random samples form non populations. In each case, use the non pooled t-fest and the non pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x~1=20,s1=4,n1=10,x~2=18,s2=5,n2=15.

a. Right-tailed test,localid="1651298373729" 伪=0.05.

b. 90%confidence interval.

You know that the population standard deviations are not equal.

In this Exercise, we have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-lest and the pooledt-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
x炉1=20,s1=4,n1=20,x炉2=24,s2=5,n2=15

a. Left-tailed test, 伪=0.05

b. 90%confidence interval

In this Exercise, we have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-lest and the pooledt-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
x炉1=20,s1=4,n1=30,x炉2=18,s2=5,n2=40

a. Right-tailed test, 伪=0.05

b. 90%confidence interval

The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months.

At the 5% significance level, do the data provide sufficient evidence to conclude that the meantime served for fraud is less than that for firearms offenses? (Note: x炉1=10.12,s1=4.90,x炉2=18.78, and s2=4.64.)
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