Question

56. + -/5 points ASWSBE14 10.E.013. My You may need to use the appropriate appendix table or technology to answer this question. The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars Private Colleges Public Colleges 52.8 44.2 45.0 32.3 45.0 20.3 22.0 28.2 15.6 24.1 28.5 30.6 45.8 | 37.8 51.5 42.0 22.8 25.8 18.5 25.6 14.4 21.8 (a) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.) sample mean $ thousand sample standard deviation $ thousand Compute the sample mean (in thousand dollars) and sample standard deviation in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.) sample mean thousand sample standard deviation $ thousand " (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private - Public.) thousand Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges. We estimate that the mean annual cost to attend private colleges is $ more than the mean annual cost to attend public college (c) Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private - Public. Round your answers to one decimal place.) thousand to $ thousand

Answer 1

solution : na to, = + (528444-04454 3223 +45+30644505 + 378454.5+43) . n = 4267 SP= Exia) L1 (528-42.71 + (442-427t- -----+(12=42+)). Si= 53:44 CS Scanne Stwito 7.236. CamScanner

→ Public College na=18 2013+ 22+28:2+15.6t 24.14 28.5 +22+8+25187 18.57256+144 2118) y = 22.3 V : s- € (417)=+[C20-3-20.3) 423037 - S = 20-su - - +(31-8-29-3)]. Standard deviation Se = 5 ss = 4.532V → Nun hypothesis (Ho) = My=M2, → Affeinate hypothe dis (Hi) != M; # 12, - Level of significance (2) - 0.05 ) population difference S= 7.236–4:532= 2.704 - Test statistic t=arty 4207-2213 SA 7.230274153 .. . It = 7.587 " dif (nitor-2) = 10412-2=20 attoos io 16725 The calculated f tabulated t fence we reject the null hypothesir (HO) Concont- - There is significant differ b/w private Cs College Bp it public college. CamScanner

c) 95% confidence interval L 4 (1-7) 41.96(sie of (1-1)] Sie of C#-) = 1osad = 2.635 (42.7-22.3) + 1196 (21635) (14835, 25.164) 12 The lower limit = 14.835 v upper limit = 25.164 v cs Scanned with CamScanner
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