Answer :
As there is less ambiguity when the population's standard deviation is known, the z interval with a value of 2.57 is preferable (the interval is too wide).
However, there is more uncertainty when the standard deviation is unknown, thus the t interval of 1.96 is more reasonable (the z-interval is too small). A z interval is a special kind of confidence interval that provides a range of possible values for a given mean or proportion. It can be determined using a standard deviation that is known. Calculate a t-interval when you don't know the standard deviation but still need to obtain a confidence interval. The only difference is that the interval is calculated using a different table: a t-table for a t-interval and a z-table for a z-interval. For more on the exact distinctions between the “T” and “Z”, see: T-scores vs. Z-scores.
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