Math Problem Statement
Conduct the stated hypothesis test for μ 1− μ 2. μ 1− μ 2. Assume that the samples are independent and randomly selected from normal populations with equal population variances ( σ 12= σ 22)( σ 12= σ 22).
H0 : μ 1− μ 2=0H0 : μ 1− μ 2=0
H1 : μ 1− μ 2 < 0H1 : μ 1− μ 2 < 0
α =0.005 α =0.005
n1=29n1=29
x̄ 1=8.51 x̄ 1=8.51
s1=1.26s1=1.26
n2=23n2=23
x̄ 2=9.36 x̄ 2=9.36
s2=1.35s2=1.35
T-Distribution Table
a. Calculate the test statistic.
t=t=
Round to three decimal places if necessary
b. Determine the critical value(s) for the hypothesis test.
Round to three decimal places if necessary
c. Conclude whether to reject the null hypothesis or not based on the test statistic.
Reject
Fail to Reject
Solution
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Two-Sample T-Test
Pooled Variance
Formulas
Test Statistic t = (x̄1 - x̄2) / sp √(1/n1 + 1/n2)
Pooled Standard Deviation sp = √[((n1 - 1)s1^2 + (n2 - 1)s2^2) / (n1 + n2 - 2)]
Theorems
Central Limit Theorem
T-Distribution
Suitable Grade Level
Undergraduate Level - Statistics