Answer:
There is no significant evidence to support the claim that college women have more credit card debt than college men
Step-by-step explanation:
Given :
women n1 =32 x1= 781 s1 = 1489 men n2 = 38 x2 = 435 s2 = 1026
H0 : μ1 = μ2
H0 : μ1 > μ2
Assume unequal variance :
The test statistic :
(x1 - x2) / √(s1²/n1) + (s2²/n2)
T= (781 - 435) / √(1489²/32) + (1026²/38)
T = 346 / 311.42740
Test statistic = 1.111
Degree of freedom, df
(s1²/n1+s2²/n2)²÷1/(n1-1)*(s1²/n1)²+1/(n2-1)*(s2²/n2)²
The Pvalue :
(s1²/n1+s2²/n2)² = ((1489²/32) + (1026²/38))² = 9406484230.6884765625
1/(n1-1)*(s1²/n1)²+1/(n2-1)*(s2²/n2)²:
1/31(1489^2/32)^2 + 1/37(1026^2/38)^2 = 1.755926E8
df = 9406484230.6884765625 / 1.755926E8 = 53.569
df = 54
The Pvalue, from t score ;
Pvalue(1.111, 54) = 0.136
Pvalue > α ; Hence, we fail to reject the null ; There is no significant evidence to support the claim that college women have more credit card debt than college men
