Is this ever possible using standard statistics techniques?

What about if you're performing complex survey analysis where the survey is stratified, clustered and weighted? I ask because I've been using SAS to process data from a complex survey design and I've run into a situation where the P-Value and 95% CI conflict:

Sample Size = 3,618

**Rao-Scott Chi-Square Test**

Pearson Chi-Square 4.1614

Design Correction 1.0794

Rao-Scott Chi-Square 3.8551

DF 1

Pr > ChiSq 0.0496 *** significant

F Value 3.8551

Num DF 1

Den DF 1765

Pr > F 0.0498 *** significant

**Odds Ratio (Row1/Row2)**

Estimate 95% Confidence Limits

Odds Ratio 0.1548 (0.0176-1.3595) *** not significant