1. For the single mean & proportion Confidence Interval vs Hypothesis Testing
At the same level in confidence interval and hypothesis testing, when the null hypothesis is rejected, the confidence interval for the mean and proportion will not contain the hypothesized mean/proportion.
Likewise, when we fail to reject null hypothesis the confidence interval will contain the hypothesized mean/ proportion.
** Applies only for two-tailed test.
Allan Bluman, pg. 458

2. For the difference of means & proportions Confidence Interval vs Hypothesis Testing
[-8.5 , 8.5]
Contains zero =
If the CI contains zero, we fail to reject H0
(Means that the there is NO DIFFERENCE in population means or proportions)
[5.45 , 12.45]
No zero
If the CI does not contain zero, we reject H0
(Mean/proportion for population 1 is GREATER than the mean/proportion for population 2)
[-7.3 , -3.3]
(Mean/proportion for population 1 is LESS than the mean/proportion for population 2)
** Applies only for two-tailed test. Eg. in Allan Bluman, pg