Question

When the population mean is unknown we might construct a confidence interval as a way of thinking about what the population mean might be.

In that construction we sometimes use a Z value and sometimes we use a t value.

In a full sentence state when we use Z and when we use t.

Answer 1

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We use Z interval when :

The sample size is greater than or equal to 30 and Population standard deviation is KNOWN OR original population normal with the population standard deviation known.

We use t interval when :

Population standard deviation is UNKNOWN and original population normal OR sample size greater than or equal to 30 and Population standard deviation is UNKNOWN.