# Self study question on Confidence Interval

I am attempting a self study question on confidence interval. My answer worked out to be $20.4 \pm 1.411$. However, the model answer appeared to be $20.4 \pm 1.486$. I am pretty confidence that I am correct. I'd appreciate if anyone could give me some advice and validation please?

Question

The owner of a big egg farm wants to estimate the mean number of eggs laid per chicken. A sample of 25 chickens shows they laid an average of 20.4 eggs per month with a standard deviation of 3.6 eggs per month. Assume the number of eggs laid per chicken per month has a normal distribution. Construct a 95% confidence interval estimate for the population mean number of eggs laid per chicken per month.

Attempt

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Yes, the estimated standard deviation means you use a t-interval. Unfortunately, using pivotal quantities as a way to construct intervals is usually not taught at this level. (I say unfortunately because framing it that way makes it pretty obvious why it must be $t$ and not $z$.) – Glen_b May 4 '14 at 21:12