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Chapter 13: Q.13.31 (page 533)

Suppose that the variable under consideration is normally distributed in each of two populations and that the population standard deviations are equal. Further, suppose that you want to perform a hypothesis test to decide whether the populations have different means, that is, whether μ1≠μ2. If independent simple random samples are used, identify two hypothesis-testing procedures that you can use to carry out the hypothesis test.

Short Answer

Expert verified

The t- test and the z- test are two different tests for comparing population means.

Step by step solution

01

Given Information

The variable being studied has a normal distribution.

The standard deviations of the population are also equal.

02

Explanation

Assume that the population standard deviations are the same based on the information provided.

Consider the following hypothesis:

Null hypothesis H0:μ1=μ2

Alternative hypothesis Ha:μ1≠μ2

Under Null hypothesis, the t-test is defined as

t=x1¯-x2¯sp1/n1+1/n2

≈tn1+n2-2

The pooled standard deviation sp=n1-1s1+2n2-1s22n1+n2-2

Under Null hypothesis, the z-test is defined as

z=x1¯-x2¯σ1/n1+1/n2

z≈N(0,1)

The population standard deviation σ=σ1,

σ=σ2

As a result, both tests can be used.

t- test and z - test.

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