You have been contracted from a company to do a study. From previous experience with the populations, it is known that the variance for population 1 is 100 and the variance for population 2 is 64. You decide to collect 100 samples from population 1 and found that the mean was 70. You also take 100 samples from population 2 and the mean of that sample is 68. The company has told you that they believe there is a difference in means. a.) Conduct a hypothesis test to find if there is any difference in means with alpha

A. find the power of the test, when the null hypothesis assumes a population mean of mu = 450, with a population standard deviation of 156, the sample size is 5 and the true mean is 638.47 with confidence intervals of 95 b. find the power of the test, when the null hypothesis assumes a population mean of mu = 644, with a population standard deviation of 174, the sample size is 3 and the true mean is 744.04 with confidence intervals of 95% c. find the power of the test, when the null hypothesis assumes a population mean of mu = 510, with a population standard deviation of 126, the sample size is 10 and the true mean is 529.44 with confidence intervals of 95