Two independent random samples have been selected, 170 observations from population 1 and 170 from population 2. Sample means $\bar{x}_1$=78 and $\bar{x}_2$=64 were obtained. From previous experience with these populations, it is known that the variances are $\sigma^2_1$=121 and $\sigma^2_2$=49. Test the null hypothesis $H_0$ : ($\mu_1-\mu_2$)=5 against $H_1$ : ($\mu_1-\mu_2$)?5, using both the p-value and rejection region approach. Use $\alpha$=0.05. Find a 95% confidence interval and interpret your results.