Question

The attached data contains a sample of undergraduate institutions in the US along with information about whether they are public or private schools and their yearly tuition costs. Your goal is to perform a hypothesis test to asses the claim that on average public schools cost less per year than private schools (using an α = 0.05 significance level).

TYPE	COST/YR ($)
Public	14434
Public	10595
Public	5558
Public	22011
Public	6499
Public	14650
Public	15935
Public	23175
Public	7640
Public	4485
Public	6129
Public	10002
Public	18218
Public	10849
Public	4116
Public	7109
Private	20585
Private	18425
Private	13975
Private	13603
Private	10744
Private	26245
Private	12071
Private	21160
Private	19114
Private	23541
Private	11399
Private	22671
Private	17091
Private	11762
Private	13471
Private	24072
Private	17173
Private	10086
Private	24221
Private	17621
Private	15569
Private	32580
Private	13812
Private	17494
Private	37606
Private	14036
Private	34243
Private	31172
Private	26602
Private	6433

a) State the Hypotheses (5 pts)		H_0
		H_a
b) Give the sample means, sample standard deviations, sample sizes and degrees of freedom (5 pts)		x_bar1
		s1
		n1
		x_bar2
		s2
		n2
		df
c) Calculate the test statistic (5 pts)		t

Answer 1

type cost/year type x2 <2 (x1- mean(x1)) 3096.19 (x2- mean(x2)) 1305.1 (x1. mean(x1)) 9586392.52 551766.70 33406203.64 (x2- mean(x2))2 1703286.01 730854.01 20585 18425 -742.81 -854.9 13795 -5779.81 -5484.9 30084128.01 13603 10673.19 -5676.9 113916984.78 32227193.61 10744 72861588.81 -4838.81 3312.19 23414082.22 10970602.60 26245 48512618.01 12071 21134155.90 21160 public public public public public public public public public public public public public public public public 4597.19 11837.19 -3697.81 -8535.9 6965.1 -7208.9 1880.1 - 165.9 4261.1 -7880.9 3391.1 51968239.21 3534776.01 27522.81 19114 23541 11399 22671 17091 -6852.81 -5208.81 -1335.81 6880.19 140119067.10 13673798.80 46961004.90 27131701.62 1784388.36 47337014.44 238935.22 52154539.68 17882834.02 -2188.9 x1 14434 private 10595 private 5558 private 22011 private 6499 private 14650 private 15935 private 23175 private 7640 private 4485 private 6129 private 10002 private 18218 private 10849 private 4116 private 7109 private private private private private private private private private private private private private private private 181405 18156973.21 62108584.81 11499559.21 4791283.21 56518820.41 33743319.21 22964222.41 4439027.61 11762 -7517.9 13471 24072 -488.81 -7221.81 -4228.81 -5808.9 4792.1 -2106.9 -9193.9 17173 10086 84527797.21 24414469.21 4941.1 -1658.9 2751949.21 24221 17621 15569 32580 -3710.9 13770778.81 13300.1 13812 -5467.9 17494 37606 -1785.9 18326.1 14036 -5243.9 176892660.01 29897930.41 3189438.81 335845941.21 27498487.21 223894361.61 141422042.41 53613148.41 165042839.61 34243 14963.1 31172 11892.1 26602 7322.1 6433 - 12846.9 total 578397 560263472.44 451432968.96

(a) we have to test the claim that public schools cost less than private schools thus, null and alternative hy bethese are Hoi MzM2 Hi! My CMa lone-talled) (b) sample mean for public schools EXI he 181405 2= 11337.81 for private schools ng ΣΥΣ 578397 30 kg = 19279.9

sample standard deviations for public scheel 3} I {xi-xej? nil こ 560263472, 44 15 2 se - 373 50898:16 Si= 6111:54 for private school 2 {ag-X ² ng 1 - 421886368:27 29 = 14547805.80 egz 3814.16 sample sizes for public schools ny=16 for private schools n = 30

dofi for testing the difference of two means the test statistic xit to sp Sthuth na follours t-distribution with (hitha-2) dif thes def. chithg-2 = 16+ 30-2 elit. = 44 (C) value of test statistic z-ig to Sp V t the where, s = pooled variance E per a 2 + 2(xe-x² (hinna-2) 22

s s ।। 560263 412.44+ 421886368.२१ 44 2 - 22321587.28 Se - 47.57 therefore, *: 11332,01-19219.9 4१२4.57 (+ - -7949.09 492457x0.31 794.09 (46462 - 2 -5.42