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.)

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.