Calculating the P-Value

In the box below, please enter the value of 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 t = 0.3656. 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 couple symbols to know:

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Thus, the p-value for these data and this hypothesis is 0.3656. As this p-value is greater than the usual α = 0.05, we fail to reject the null hypothesis at that level. What we observed is reasonably common if the null hypothesis is true.

Show the R Code

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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 that follows “p-value =” near the top. Note that R will give you p-values that are more accurate and more precise than doing the calculations by hand. As such, these computer-calculated limits may differ slightly from those you calculate by hand.

Show the Excel Code

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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 sample1 ends up in A1 after pasting.

The test statistic is the number calculated in cell D6. The p-value is in cell D7. Again, when you paste this code into Excel, make sure that you start the pasting in cell A1. To help with that, you may want to also copy this notice. It seems to help.