Question

Two samples are randomly selected from each population. The sample statistics are given below. Find the P-value used to test the claim that H, H2. Use c = 0.05. ng = 100, n2 = 125, X= 615, x2 = 600, 6, = 40,02 = 24 O A. 0.0005 OB. 0.5105 OC. 0.1015 OD. 0.0505

Answer 1

Ans. 1)

The test statistic and the p-value are computed as follows

$\\Z_{0} = (\bar{x_{1}}-\bar{x_{2}})/\sqrt{{s_{1}}^{2}/n_{1}+{s_{2}}^{2}/n_{2}} \\ Z_{0} = 3.3042\\ p-value = Prob (Z > Z_{0} ) = 0.000476 \simeq 0.0005$

Correct Ans: (A) 0.0005

Ans.2)

Hypotheses in Option (B) are correct.

$\\F_{^{STAT}} = (s_{1}^{2}/(n_{1}-1))/(s_{2}^{2}/(n_{2}-1))\\ = 1.455093 \\p-value = Prob(F > F_{^{STAT}}) = 0.97605$

p-value > 0.05. Hence, we have to accept H0. There is insignificant evidence of a difference in the variance.

Ans.3(a)

95% confidence interval for the mean is (20.86802,21.08198).

Ans.3(b)

Option (C) is correct.

Hope this helps!