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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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2 Answers 2

up vote 4 down vote accepted

You are almost correct. If you had a larger sample of chicken, your attempt would have been correct. However, even though you report normality, you could still adjust for your smaller sample size by using a different distribution.

  • What distribution is used for small sample sizes?

When you use the appropriate formula for CIs built from that distribution, you will find that you need a slightly different critical value, which will result in a slightly wider CI.

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After taking into consideration @jona's comments, I managed to work out the answer to be the following:

enter image description here

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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 at 21:12
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