Question

A random sample of 49 measurements from one population had a sample mean of 18, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 21, 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. The standard normal. 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 known standard deviations. . 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. (b) State the hypotheses. o Ho: M1 = 42; H1: M1 < u2 . Ho: M1 = uz; H1: 41 > uz . Ho: M1 + M2; H1:41 = 42 . Ho: M1 = M2; H1:41 # M2 (c) Compute 71 - 72 x1 - x2 = Compute the corresponding sample distribution value. (Test the difference uy - My. Round your answer to three decimal places.)

Answer 1

Sample! X=48 s,=5 ne-49 Sample 2 - 21 S2 = 6 mg 64 Ho: M = 42 Ha! M, EN *, - x= 18-21 3-3 Sample statistic value = (x-x2)-(4,4) S +के where Spa Sh1n, -1) + 5, 10,-1) 25x48 + 36*6 - Sp=1156 > Sp=5.5896 - nth 2 49+64-2 Itz 37 -3 . C.5896 LtI ✓ 49 64 - = -.827 It Enticed Coitical value at 2=0.01 It athar, d = 1 t11,9005 + 2.621 Reject Hay t 72.621 or t <-2.621 Since t <-2,621 we repet to and 1. [-2.827) concluded that there is difference in two means.