Answer
No, the results of the January poll do not indicate that the proportion of Americans who approve of the job Obama is doing is significantly higher than December’s level.
Work Step by Step
Here we have: $H_{o}$: p = 0.48, $H_{a}: p > 0.48$, n = 1500, p = 0.48, $\hat p =747/1500 = 0.498$
Checking the model requirements:
np(1-p) = 1500 x 0.48 (1 - 0.48) = 374.4 > 10
$z = \frac{0.498 - 0.48}{\sqrt \frac{0.48(1-0.48)}{1500}} = \frac{0.018}{0.0129} = 1.395$
P(z > 1.395) = 0.0815
This implies that 8 out of 100 samples will have a proportion of more than 0.48.
