Shifting the Sample Mean | Montgomery College, Maryland

ACTIVITY

A 2013 article on NPRnew window quoted that users unlock their phones an average of 110 times a day. Could that number be higher for users today? We don't know the average number of unlocks for users these days. Let's call this average, µ. We want to test if µ > 110. The null hypothesis is µ = 110, which says that the average today is no different that the average in 2013.

StatKeynew window method for performing a randomization test for a mean to test claims about a population mean involves shifting the sample mean by a certain amount so that the shifted mean equals the null hypothesized population mean.

In this activity, you will take a sample dataset of Number of Screen Unlocks and shift its mean to equal the null mean.

PROCEDURE

STEP 1: Open a blank worksheet on Miscrosoft Excel or an online spreadsheet prograom such as Google Sheets or Excel online.

Don't have Microsoft Excel? Go to Office 365 for Studentsnew window to obtain yours for free (for MC students).

STEP 2: Open the sample datanew window to access the Number of Screen Unlocks data. Select the data to copy and paste the data into the worksheet you opened in STEP 1.

STEP 3: Calculate the sample mean, x̄.

» Click on an empty cell below your data and type: =AVERAGE(

» Select the first cell containig your data, hold the left button down on your mouse and drag down to select all the cells containing your data and hit ENTER.

STEP 4: Calculate the difference between your sample mean, x̄, and the null mean, µ: Difference = x̄ – µ.

STEP 5: Add this difference (or subtract if the difference is negative) to each data value in your dataset.

» Click on a blank cell to the right of the first data value in the dataset and type: =

» After typing the equal symbol, click on the cell containing your first data. Your cell should read something like =A2 at this point.

» Next type the + symbol and enter the difference you calculated in STEP 4. Your cell should read something like =A2 + #### at this point, where #### is the difference from STEP 4.

» Hit ENTER to see the result, and click on the same cell again. Now, double click on the green square on the bottom right of the selected cell to copy the formula down the column.

STEP 6: Calculate the average for this column to make sure the average is 110.