Minitab uses exact methods to make inferences about binomial proportions. You can choose to use a normal approximation by clicking Options, and choosing Normal approximation in the dropdown beside Method. Most textbooks use the normal approximation method because it is easy for students to calculate manually. However, the exact methods are usually more reliable than the normal approximation method.
With the normal approximation, it is possible to get different conclusions between the p-value and the confidence interval. This is because this method uses the hypothesized probability (ρ0) in the calculation of the test statistic and the observed probability (estimated proportion) in the calculation of the confidence interval. This could cause a difference between the conclusions, especially with larger values of Z which would indicate a large difference between ρ0 and the population proportion.