寝てない is a very common contraction of 寝ていない, where there is a subsidiary verb いる. See this chart. To clarify, the simple nai-form of 寝る is 寝ない, since 寝る is a vowel-stem (aka ichidan) verb.

いる in this case is analogous to English present perfect aspect (eg, "have slept"), which describes the continuation of some state (in your sentence, sleeplessness). See the discussion in this question: When is Vている the continuation of action and when is it the continuation of state?

You would probably say to someone who just woke up, using the past tense:

よく寝た? Did you sleep well?

But when you see someone who looks sleepy at work, something like this is more likely to be heard:

昨日あまり寝てないの? Haven't you slept well last night?

寝てない is a very common contraction of 寝ていない, where there is a subsidiary verb いる. See this chart. To clarify, the simple nai-form of 寝る is 寝ない, since 寝る is a vowel-stem (aka ichidan) verb.

いる in this case is analogous to English present perfect aspect (eg, "have slept"), which describes the continuation of some state (in your sentence, sleeplessness). See the discussion in this question: When is Vている the continuation of action and when is it the continuation of state?

You would probably say to someone who just woke up, using the past tense:

よく寝た? Did you sleep well?

But when you see someone who looks sleepy at work, something like this is more likely to be heard:

昨日あまり寝てないの? Haven't you slept well last night?