Using either the critical value rule or the p-value rule, if a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i. e., the same sample size, the same standard deviation, and the same mean) will be rejected at the same significance level.

Step-by-step explanation:

In hypothesis testing if p value < alpha i.e. our significance level we reject null hypothesis

Consider for example, 95% confidence level is taken, and p value one tailed is 0.026. Since p <0.05, We reject null hypothesis

p value two tailed is twice p value for one tailed.  Hence p value two tailed =0.052.  

Since p value >0.05 our alpha.  So in this case, null hypothesis will be accepted

Hence sometimes it would be rejected and sometimes it would be accepted

Using either the critical value rule or the p-value rule, if a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) need not   be rejected at the same significance level.