Question

A random sample of n = 10 regions in New England gave the following violent crime rates (per million population). x New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x, Rocky Mountain Crime Rate 3.7 4.1 4.7 5.1 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. (1) Use a calculator to calculate X, S, Xy, and sz. (Round your answers to two decimal places.) Eix six (ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. HO:H1 = 12; H1: M1 M2 HO: Hy <H2; M: 41 = 42 Ho: 41 = My; Hy: My > M2 Ho: M1 = Hy; H4:41 # Hz (b) What sampling distribution will you use? What assumptions are you making? The Student's t. 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 standard normal. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference - Hly. Round your answer to three decimal places.)

Answer 1

Crime Rocky Mountain crime 1 (1 New England no 10 X = 3.5l s =0.832 12 = 12 X = 3.85 S₂ = 0.926 1)(a)x= 0.01 is the level of significance Ho : X ع 21 = % 4 رکھی ہر M, is the population mean of new Englured crime M2 is the population mean of Rocky mountain crime (62 The student's f, we assume that both population desforbutions are normal approximately Nonmul with canknown standard deviations. Tesh statiste us f = t - Xe Jo-1 st. 102-15² +,-2 - = -0.34 = -0.898 - Voor (C) P-value = P[t<-00898 ] = 0.1899 le 0-12 5< P-value <0.260 -fa-00898 ed. At the x-0001 level, are fail to releet the null hapothesis and Concluded the dat are not Stuhiahicaly siymficant Copsion al 2 fail to relect the null bypothesis, these is evidence shut riolent crime in the in sufficient Rockey mountain regue is higher than in New Grylend. crine Copbrond). I wa