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Student's t-distribution - Confidence Intervals

Student's t-distribution


In the previous section we discovered how to make a confidence interval for estimating population mean. However we knew what the population standard deviation (σ\sigma) was. However it is not always the case that σ\sigma is known.

If population standard deviation (σ\sigma) is unknown then to make a confidence interval to estimate population mean we cannot our old formula for error: E=Zσ2σnE=Z_\frac{\sigma}{2}*\frac{\sigma}{\sqrt{n}} as it requires a knowledge of σ\sigma. So instead we are required to use a thing called t-scores (tα2)t_{\frac{\alpha}{2}}).

Once we find the t-scores for particular values (this is done in a similar way to finding z-scores) we have a new formula for the Margin of Error:
  • 3.
    In “Anchiles”, a small made-up town near the equator, 15 random days were sampled and found to have an average temperature of 28°C, with a standard deviation of 4°C. Assume that the average daily temperature of this town is normally distributed.
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Student's t-distribution

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