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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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: What 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.
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: H1# H2i H;: H1 = H2
O Ho: H1 = H2 Hq> H2
O Ho: H1 = H2i H;: Hq # Hz
O Ho: H1 = H2i Hị: H1< Mz
(c) Compute x, - X2.
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.)
Transcribed Image Text: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: What 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. 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: H1# H2i H;: H1 = H2 O Ho: H1 = H2 Hq> H2 O Ho: H1 = H2i H;: Hq # Hz O Ho: H1 = H2i Hị: H1< Mz (c) Compute x, - X2. 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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