Answer:
Answer:
1. The confidence interval for the difference of means weight gain using 76 as the degree of freedom is -1.664, 5.664
2.The calculated value of t does not lie in the critical region for both d.f 76 and 83 . Therefore we accept our null hypothesis that pigs fed with Diet A gain more weight than with diet B at the 0.05 level
Explanation:
# Pigs Mean Weight Gain Standard Deviation
Diet A 36 55 3
Diet B 49 53 5.6
(x`1- x` The 2) ± t∝/2 (v) . Sp √1/n1 + 1/n2
where v= d.f= 76
Here the difference between the sample means is x`1- x`2= 55-53= 2
The pooled estimate for the common variance σ² is
Sp² = 1/n1+n2 -2 [ ∑ (x1i - x1`)² + ∑ (x2j - x`2)²]
= 1/36 +49-2 [ 55²+53²]
Sp = √3025 +2809/83 = 8.38
t (0.025) (76) = 1.992
(x`1- x`2)± t∝/2 (v) . Sp √1/n1 + 1/n2
(2 )± 1.992 (8.38) √ 1/36 + 1/49
(2 )± 3.664
-1.664, 5.664
Par t 2:
The null and alternate hypotheses are
H0 : u1 > u2 against Ha: u1 ≤ u 2
Significance level alpha = 0.05
The critical region t ≥ t (0.05, 76) = 1.665
D.f = n1+n2- 2= 83
The critical region t ≥ t (0.05, 83) = 1.663
t = (x`1- x` ) /. Sp √1/n1 + 1/n2
t= 2/ 8.38 √1/36+ 1/49
t= 2/1.839
t= 1.087
The calculated value of t does not lie in the critical region for both d.f 76 and 83 . Therefore we accept our null hypothesis that pigs fed with Diet A gain more weight than with diet B at the 0.05 level