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In: Statistics and Probability

Suppose you want to test the claim that μ1 = μ2. Two samples are random, independent,...

Suppose you want to test the claim that μ1 = μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that σ 2 1 = σ 2 2. At a level of significance of α = 0.05, when should you reject H0?
n1 = 14 n2 = 12 x1 = 21 x2 = 22 s1 = 2.5 s2 = 2.8

Solutions

Expert Solution

Hypothesis: (Claim) Vs  

Now use the t-test.

The test is two-tailed test

The pooled estimate is ,

df=degrees of freedom =n1+n2-2=14+12-2=24

The test statistic is ,

The critical values are ,

; From t-table

Decision : Here , the value of the test statistic does not lies in the rejection region

Therefore , fail to reject Ho.

Conclusion : Hence , there is sufficient evidence to support the claim.

orchestra answered 2 years ago
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