A random sample of 49 measurements from a population with population standard deviation of = 3 had a sample mean of x1 = 13. An independent random sample of 64 measurements from a second population with population standard deviation 62 = 4 had a sample mean of x2 = 15. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. O The standard normal distribution. Samples are independent, the population standard deviations are known, and the sample sizes are sufficiently large. O The student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The student's t. We assume that both population distributions are approximately normal with known standard deviations. (b) State the hypotheses. O Ho: #1 = #2; H1: H1 > H2 O Ho: #1 = M2; H1: M1 # #2 O Ho: #1 # 12; H1: H1 = M2 O Ho: H1 = H2; H1: M1