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Z-Procedures
Example #450: Let us estimate the mean height of a population, using a confidence interval to indicate our level of uncertainty. To estimate μ, we collect data. These data are the heights of a sample from this population. The sample values are:
78, 73, 77, 53, 72, 81, 82, 61, 78, 63, 72, 60, 50, 87, 76, 51, 70, 89, 75, 72, 73, 78, 66, 75, 42, 76, 69, 60, 83, 80, 82, 62, 78, 76, 66, 72, 75, 70, 52, 62, 65, 86, 56, 62, 81, 76, 74, 90, 60, 67, 75, 88, 62, 74, 63, 81, 69, 59, 67, 85, 62, 76, 73, 87, 80
In addition to these data, we also know that the data are generated from a Normal process (they come from a Normally distributed population) and that the standard deviation of this population is σ = 11. With this information, let us estimate the population mean using a 90% confidence interval.
To summarize the above, the values of import are:
\( \bar{x} \) | = | 71.3077 |
---|---|---|
\( \sigma \) | = | 11 |
\( n \) | = | 65 |
\( \alpha \) | = | 0.1 |
Note that there is no value given for μ0. This is because confidence intervals are based solely on the data, and not on any hypothesized values.
It may be helpful if you calculate these values yourself. Once you have, you can check your answers by hovering your mouse over the grey spaces to see if you calculated them correctly.
In the box below, please enter the two endpoints of the 90% confidence interval for the population mean, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
90% Confidence Bounds: (, )
Make sure the lower limit is less than the upper limit.
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