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2.1: Examples for Later

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Example $$\PageIndex{1}$$

In statistics we often want to compare a computed value to see whether it is less than or greater than 5%. This value is called the p-value. Suppose the calculator gives us that the p-value is 0.0413. Convert this value to a percent and decide how it compares to 5%.

Solution

We move the decimal 0.0413 two places to the right to get

4.13%

We can now see that 4.13% is less than 5%.

(not for this section, but keeping for now until I work on the order of operations section)

Example $$\PageIndex{7}$$

The "z-score" is defined by:

$$z=\frac{x-\mu}{\sigma}$$

Find the z-score rounded to one decimal place if:

$$x=2.323,\:\mu=1.297,\:\sigma=0.241$$

Solution

We can put these numbers into the z-score formula and use a computer or calculator to get

$$\frac{2.323-1.297}{0.241}\:=\:4.25726141$$

Now round to one decimal place to get 4.3. Notice that if you rounded before you did the arithmetic, you would get exactly 5 which is very different. 4.3 is more accurate.