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A random sample of 49 measurements from one population had a sample mean of 14, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 17, with sample standard deviation 6. 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 Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. O Ho: H1 = H2; H1: H1 > H2 O Ho: H1 = Hzi Hj' HIS H2 (c) Compute X, - X,. x 1 - X , = Compute the corresponding sample distribution value. (Test the difference , - (,. Round your answer to three decimal places.) (d) Estimate the P-value of the sample test statistic. O P-value > 0.500 O 0.250