Question

3

0.0232-20 2.3201 2) The critical value for a right-tailed F test is 2.57 (rounded to two decimal) when 2 B a=0.025, the degrees of freedom for the numerator are 15, and the degrees of freedom DIS for the denominator are 20. A) False (B) True 2.573 cv. 1.5 Test the indicated claim about the variances or standard deviations of two populations. Assume that the populations are normally distributed. Assume that the two samples are independent and that they have been randomly selected 3) Test the claim that populations A and B have different variances. Use a significance level of 3) 0.10. 5) 0.05 Dri:27 OiOS Df2 : 40 0.05 Sample A Sample B n=28 n=41 x1 = 19.2 x2 = 23.7 S =4.7 s = 5.89 1) claimi a =a² -> (Ase 1/2 2) Hoia, - az 3) Hi alfa, tovo tail 72 = 22.09 = 0.6367 5.89² 34.6921 ñ 0 164 0.10/2, 17929 couclingy = 0.05 6) Fail to meject Ho -> CAS e 2 7) No sufficient evident to support the claim a= a. 4) A random sample of 16 women resulted in blood pressure levels with a standard deviation 4) of 22.1 mm Hg. A random sample of 17 men resulted in blood pressure levels with a standard deviation of 20.8 mm Hg. Use a 0.025 significance level to test the claim that blood pressure levels for women have a larger variance than those for men. monili ) claim an> 92 -Y CASE 3 Oy

Answer 1

3)

Null and alternative hypothesis:  
Hₒ : σ₁² = σ₂²  
H₁ : σ₁² ≠ σ₂²  

Test statistic: taking large variance in numerator ,  
F = s₁² / s₂² = 5.89²/4.7² = 34.6921 / 22.09 =    1.5705

Degree of freedom:  
df₁ = n₁-1 =    40
df₂ = n₂-1 =    27

α=0.10
Critical value(s):  
Lower tailed critical value, FL = F.INV(0.1/2, 40, 27) =    0.5661
Upper tailed critical value, FU = F.INV(1-0.1/2, 40, 27) =    1.8361

since, test test falls between two critical value , fail to reject Ho

there is no enough evidence to conclude that two population variance are different