Question

Given two dependent random samples with the following results:

Population 1. 54 83 68 66 62 60 70 62

Population 2. 59 74 76 64 64 69 67 64

Can it be concluded, from this data, that there is a significant difference between the two population means? Let d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.01 for the test. Assume that both populations are normally distributed.

Step 2 of 5 : Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places

Step 5 of 5: Make the decision for the hypothesis test. Reject or Fail to regect Null Hypotthesis.

Answer 1

Solution- step: 1 nuce hypothesis : ly = 0 Alternate hypothesis : ld to * For o.ol level with a failed test & nal= 7 degree of freedom, critical value of t= 3.4995 * Decision Seele: repect Hoof absolute value g test statistic it1>3.499 S.NO population i population 2 diftedenle id) Id:X-X2 54 59 25,000000 83 74 81.000000 68 76 64.000000 .66 64 4.000000 64 4.000000 60 69 81.000000 10 62 64 67 9.000000 4.000000 Total Eda-na Ed²=272 n=8 Mean abar= - 1.500 degree g freedom and = 7.000 standard deviation Sp= {{d²_(Ed)²/n]/(0-1) 16-12€-6272)/8] / + = 6-0038

std error = Se : Solra 26.0238117.000 = a.1997 Test statistic - Co-ed] /se = -0.7043 Step ig5 Null of hypothesis ed=0 Alternate hypothesis ud to stepa: value of standard deviation ☆ the paired differences =640 value o test statiskie = -0.707 (tey-0.704 if this comes aleong) Bebes on sule: Relect Ho is t2-3-499 ás +23-499 Step 5: * fail to reject to Step 3: +3.499 i 4.3.499 ay Dec