Let 1 and 2 denote true average densities for two different

Let ?₁ and ?₂ denote true average densities for two different types of brick. Assuming normality of the two density distributions, test

State the conclusion in the problem context.

Fail to reject H₀. The data suggests no difference between the true average densities for the two different types of brick.

Fail to reject H₀. The data suggests a difference between the true average densities for the two different types of brick.   

Reject H₀. The data suggests no difference between the true average densities for the two different types of brick.

Reject H₀. The data suggests a difference between the true average densities for the two different types of brick.

Solution

The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(23.74-20.92)/sqrt(0.161^2/7+0.24^2/6)

=24.45

The degree of freedom =n1+n2-2=6+7-2 = 11

It is a two-tailed test.

So the p-value = 2*P(t with df=11 >24.45) =0 (from student t table)

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Reject H₀. The data suggests a difference between the true average densities for the two different types of brick.