Question

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.

      Ho:μ1=μ2Ho:μ1=μ2
      Ha:μ1<μ2Ha:μ1<μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data.

Sample #1	Sample #2
82.9 76 98.2 63.9 76.2 86.9 71.7 82.5 77.4 87.4 61.8 85.1 89	83 88.5 86.4 78.9 92.7 88.2 92.7 71.6 88 89.5 96.4 87.1 80.7 86.6 74.3 84.4 80.7 80.5 86.4 81.2 73.8 93

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

Answer 1

Let x Sample 1 and y. Sample 2 S.No. ly-ybar)2 3.0786 14.0280 2.7073 34.2763 63.1294 4 SE54u (x-xbar)2 829 8.8619 76 15.3907 98.2 334.0451 63.9 256.7397 76.2 13.8615 86.9 48.6771 717 67.6194 82.5 6.5404 77.4 6.3660 8724 55.9040 51.8 328.4468 26.8003 82.3901 10391251.7431| 83 88.5 86.4 78.9 92.7 88.2 92.7 71.6 88 89.5 964 87.1 80. 7 86.6 11.8708 63.1294 173.0435 10.5326 22.5188 | 135.6153 5.5009 16.4398 3.4055 109.2987 0.1257 16.4398 18.2016 27073 Total 844 80.7 805 2 270.0032 Total 1864.6 205.5745

13 12 = 104.3119 i For sample 2 , M=13, Ex= 1039 F = $x = 1034 – = 79.9231 S? E (x-70)2 - 1251-7431_ 15,2= 104,319 For sample 2 n2 = 22, Ex=1864.6, F = Er = 1864,6 = 84.7546 52 = {(y-7)2 = 906.5345 = 43.1702 (52 2 = 43.1702 na 22 SON N2-1 21 5 LO: Here we want to test Ho lli M2 VS Hoil, (42

sp=562,-1) + S₂2 (M2-1) nitt-2 =104.3119x12 + 43. 1902×21 13+22-2 = 2158.318 33 sp= 65.4036 op vri, this JB tán = 0.3498 Sp V bi tb = 8.0872 x 0.3498 = 2.8291 is The test statistic t = X-Y - sp Wh + 7 t = -)-70787 = 79.9231-84.7546 2.829) 5 t = -1708 (: Runding upto 3 decimal) The pvalue is 0.0485 using R software > Pt (-abs 61708, 33) de not-2 [1] 0.04851434 ₂0.0485