Two samples are independent and 1 ̅̅̅ = 43,1 = 23,1 = 4.5. 2 ̅̅̅ = 41,2 = 13,2 = 5.1. Consider 1: mean of population 1 2: mean of population 2 Step 1: The claim is 1 ≠ 2 Step 2: Alternative to claim is 1 = 2 Step 3: The null and alternative hypothesis are: 0: 1 = 2. : 1 ≠ 2(Claim)
Step 4: The significance level is = 0.05 Step 5: Here 1 ̅̅̅ = 43,1 = 23,1 = 4.5. 2 ̅̅̅ = 41,2 = 13,2 = 5.1.
=
(1 ̅̅̅ − 2 ̅̅̅) − (1 − 2)
√
1 2 1 +
2 2 2
=
43 − 41 √4.5 × 4.5 23 + 5.1 × 5.1 13
= 1.178
Step 6: The t- value at /2 = 0.025 and df=n-1=13-1=12 is ±2.179 (for two tailed test) Because the test statistic does not fall within the critical region, fail to reject the null hypothesis: 1 = 2.
Solution(2): Margin of error (E) is given by
= 2⁄
√
1 2 1
+
2 2 2
= 2.179√ 4.5 × 4.5 23
+
5.1 × 5.1 13
= 2.179 × 1.697 = 3.699
Hence, Confidence interval is given by (1 ̅̅̅ − 2 ̅̅̅) − < (1 − 2) < (1 ̅̅̅ − 2 ̅̅̅) +
(43 − 41) − 3.699 < (1 − 2) < (43 − 41) + 3.699 −1.699 < (1 − 2) < 5.699
الاخير
بس الثالث احد عنده خبر
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