Consider the following hypothesis test. $$H_0: \mu_1 - \mu_2 \le 0$$ $$H_a: \mu_1 - \mu_2 > 0$$ The following results are for two independent samples taken from the two populations. Sample 1 $$n_1 = 40$$ $$\bar{x}_1 = 25.5$$ $$\sigma_1 = 5.1$$ Sample 2 $$n_2 = 45$$ $$\bar{x}_2 = 22.6$$ $$\sigma_2 = 7.0$$ a. What is the value of the test statistic (round to 2 decimals)? b. What is the p-value (round to 4 decimals)? Use z-value rounded to 2 decimal places. c. With $$\alpha = 0.05$$, what is your hypothesis testing conclusion? p-value is - Select your answer - $$H_0$$
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Given values: $$n_1 = 40$$ $$\bar{x}_1 = 25.5$$ $$\sigma_1 = 5.1$$ $$n_2 = 45$$ $$\bar{x}_2 = 22.6$$ $$\sigma_2 = 7.0$$ Substitute these values into the formula: $$z = \frac{(25.5 - 22.6) - 0}{\sqrt{\frac{5.1^2}{40} + \frac{7.0^2}{45}}}$$ $$z = Show more…
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