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Z-Procedures
Example #279: Let us test the null hypothesis that the mean height of a population is 55 cm. In symbols, this is:
H0 : μ = 55 cm
To test this hypothesis, we collect data. These data are the heights of a sample from this population. The sample values are:
19, 56, 63, 66, 63, 51, 19, 69, 49, 52, 43, 62, 35, 64, 49, 51, 69, 67, 53, 39, 67, 42, 32, 63, 73, 58, 69, 65, 53, 67, 50, 80, 59, 42, 51, 66, 74, 55, 78, 61, 68, 13, 45, 61, 68, 32, 59, 78, 40, 35, 53, 59, 22, 44, 43, 55, 72, 57, 50, 71, 75, 57, 52, 45, 92, 59, 38, 68, 54, 23, 40, 48, 59
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 = 14.
With this information, calculate the test statistic corresponding to the null hypothesis.
To summarize the above, the values of import are:
\( \mu_0 \) | = | 55 |
---|---|---|
\( \bar{x} \) | = | 54.5068 |
\( \sigma \) | = | 14 |
\( n \) | = | 73 |
Calculate them yourself, then hover your mouse over the grey space to see if you calculated them correctly.
In the box below, please enter the z test statistic for the null hypothesis and the data given above. Once you have done so, click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
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