Question

You wish to test the following claim (Ha) at a significance level of a=0.01. Ho:u1=u2 Ha:p1u2 You obtain the following two samples of data. Test statistic three decimal places P value four decimal places. Accept or reject the null Sample 1 101.8 547 76.6 106.8 91.5 83.8 84.1 96.4 80.7 83.2 94.4 89.6 71.2 81.9 87.3 89.6 93.1 60.2 91.1 103.9 85.4 82.3 90 74.3 98.7 100.9 96.4 74.7 95.8 98.1 67.6 81.3 726 96.9 68.9 92.3

Answer 1

Solution-:

Here, $\sigma$ is unknown so we use t test for equality of two population by using R software as follow;

To test hypothesis

Hopi = pz
. Vs
2017 In : "H

El samplei=scan('clipboard")| Read 66 items sampler NAX 101.8 54.7 76.6 106.8 91.5 83.8 84.1 96.4 80.7 83.2 94.4 89.6 NXBN N2 81.9 87.3 89.6 93. 60.2 91.1 103.9 85.4 823 90.0 74.3 N25N 198.1 100.9 96.4 174.7 95.8 98.1 676 813|72.6 96.9 68.9 92.3 NBIN 90/4 0., 102.8 82.6|79, 773.9|7878318 V001 631 6 8 1039 NAON B5 85.1 72.6 88.6 86.6 93.1 32.9 637|807 65.2 774 98,7 K6N, 64,2 6,6 |

> sample2=scan("clipboard") Read 45 items > sample2 [1] 87.8 63.9 69.3 70.5 68.0 54.7 117.8 129,8 66.7 90.6 57.0 59.8 [13] 64.6 115.6 103.0 68.7 82.4 57.0 91.7 67.4 71.1 100.4 58.9 65.3 [25] 91.1 89.4 67.4 76.1 110.6 42.3 60.7 66.7 54.7 79.8 75.0 74.5 [37] 103.9 109.3 87.2 106.9 66.7 77.7 61.6 110.6 62.4 > nl-length(samplel).nl [1] 63

>n2=length(sample2);n2 [1] 45 > t test(samplel, sample2, var.equal=T) Two Sample t-test data: samplel and sample2 t= 1.5251, df = 106, p-value = 0.1302 alterative hypothesis: true difference in means is not equal to 0 95 perceni confidence interval: -1.454357 11.151500 sample estimates: mean of x mean ofy 83.5841379.03556 > alpha=0.01 >>=Decision Ruie: If P-value >0.01(alpha), hence we accept Hb at Los. >=Here, test statistic=t=1.525 and P-value= 0.1302

R-Program for this test samplel=scan("clipboard") samplel sample2=scan("clipboard") sample2 nl=length(samplel);nl n2=length(sample2);n2 t.test(samplel,sample2, var.equal=T) alpha=0.01 #Decision Rule: If P-value >0.01(alpha).hence we accept Ho.at Los #Here, test statistic=t=1.525 and P-value=0.1302
Note: scan("clipboard") command used for taking data from MS-Excel to R software.