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[Step-by-Step] Consider the following hypothesis test H_0:μ _1-μ _2=0 , H_A:μ _1-μ _2≠ 0 , The following results are for two independent

Question: Consider the following hypothesis test

\(\begin{aligned} & {{H}_{0}}:{{\mu }_{1}}-{{\mu }_{2}}=0 \\ & {{H}_{A}}:{{\mu }_{1}}-{{\mu }_{2}}\ne 0 \\ \end{aligned}\)

The following results are for two independent samples taken from the two populations

\[\begin{array}{ll} \text { Sample 1 } & \text { Sample 2 } \\ n_{1}=80 & n_{2}=70 \\ \bar{x}_{1}=104 & \vec{x}_{2}=106 \\ \sigma_{1}=8.4 & \sigma_{2}=7.6 \end{array}\]
  1. What is the value of the test statistic?
  2. What is the \(p\) -value?
  3. With \(\alpha=.05\), what is your hypothesis testing conclusion?

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