I need answers to: B) find the standardizrd test stastic, C) calculate P-value U

Question

I need answers to: B) find the standardizrd test stastic, C) calculate P-value

Use technology to help test the claim about the difference between two population means mu1 and mu2 at the given level of significance a using the given sample statistics. Assume that the population is normally distributed and the samples are independent and random. Assume signa21= sigma22. claim: mu1 mu 2; alpha = 0.01 Sample statistics: = 189, S1 = 37, n1 = 13 and = 191, s2 = 42, n2 = 10 Identify the null and alternative hypotheses. Choose the correct answer below'. H0 : mu1 - mu2 = 0 Ha : mu1 - mu2 0 H0 : mu1 - mu2 0 Ha : mu1 - mu2 0 H0 : mu1 - mu2

Explanation / Answer

If we let ( d = u_{1}-u_{2} ), the mean difference, and (hat{d}) represent your sample difference then the test statistic for d: (t_{hat{d}} = rac{hat{d}-d}{sigma_{hat{d}}}), where ( sigma_{hat{d}} = sqrt{rac{sigma_{1}}{n_{1}}+rac{sigma_{2}}{n_{2}}}). Thus, noting that the mean difference (or hypothesized difference) is 0:

(t_{hat{d}} = rac{hat{d}-d}{sqrt{rac{sigma_{1}}{n_{1}}+rac{sigma_{2}}{n_{2}}}} Rightarrow)

(=rac{-2}{sqrt{rac{37}{13}+rac{42}{10}}} Rightarrow )

(=-0.753).

Using an online p-value calulator, we find the p-value of -0.753 at 13+10-2=21 df is .4958.

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