A random sample of n, = 49 measurements from a population with population standard deviation o, = 3 had a sample mean of x, = 13. An independent random sample of n, = 64 measurements from a second population with population standard deviation o, = 4 had a sample mean of x, = 15. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: Wwhat distribution does the sample test statistic follow? Explain. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O P The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. 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: Hy # Hzi H;: Hy = Hz O Ho: H1 = Hzi H;i Hq> Hz O Ho: H1 = H2i Hzi Hq # Hz O Ho: H1 = H2i H;: Hq < Hz (c) Compute x-×2" x1 - x2 = Compute the corresponding sample distribution value. (Test the difference u, - Hz. Round your answer to two decimal places.) (d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)