Calculating the P-Value

In the box below, please enter the p-value 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.

Your guess:

You got the correct answer of 0.223. Congratulations!

Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.

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Here is the formula you can use to calculate the z test statistic.

In this formula, there are a few symbols to know:

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Thus, the p-value for these data and this hypothesis is 0.2230. As this p-value is greater than the usual α = 0.05, we fail to reject the null hypothesis. What we observed is reasonably common if the null hypothesis is true.

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The z-procedures are sensitive to knowing the population variance. Logic dictates that if we do not know the population mean, then we will not know the population variance. As such, the z-procedures are rarely used now. As such, there is no z-test in the base R package.

The following code will perform the above steps, however. Copy and paste the following code into your R script window, then run it from there.

In the R output, the p-value is the number output by the script.

For practical reasons, the base R installation does not contain the z-procedures. However, I have created one for pedagogical purposes. If you are connected to the Internet, the following will also calculate the test statistic:

The p-value follows “p-value =” near the top of the output.

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The z-procedures are sensitive to knowing the population variance. Logic dictates that if we do not know the population mean, then we will not know the population variance. As such, the z-procedures are rarely used now. As such, there is no z-test in the base Excel program.

Copy and paste the following code into your Excel spreadsheet window, making sure the value x ends up in A1 after pasting.

The z test statistic is the number calculated in cell C4.

Again, when you paste this code into Excel, make sure that you start the pasting in call A1. To help with that, you may want to also copy this notice. It seems to help.