STEP-BY-STEP TECHNOLOGY GUIDE: χ2 Distribution

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EXCEL

Finding the Critical Values and

  • Step 1 Select cell A1. Click the Insert Function icon fx.
  • Step 2 For Search for a Function, type chiinv, click GO, then click OK.
  • Step 3 To find : For Probability, enter (such as 0.975 for a 95% confidence interval), and for Deg_freedom enter the degrees of freedom. Click OK. Excel displays the value of in the cell.
  • Step 4 To find : Repeat Steps 1-2. For Probability, enter (such as 0.025 for a 95% confidence interval), and for Deg_freedom enter the degrees of freedom. Click OK. Exce displays the value of in the cell.

MINITAB

Finding the Critical Values and

  • Step 1 Click Calc > Probability Distributions > Chi-Square…
  • Step 2 Select Inverse cumulative probability, and enter the Degrees of freedom.
  • Step 3 To find : For Input constant, enter the area to the left of the desired critical value. For this will be (such as 0.025). Click OK.
  • Step 4 To find : Repeat Steps 1 and 2. For Input constant, enter the area to the left of the desired critical value. For this will be (such as 0.975). Click OK.
  • Step 5 Minitab displays the values of and in the session window.

Finding a Confidence Interval for σ

  • Step 1 Enter the data into column C1.
  • Step 2 Select Stat > Basic Statistics > 1 Variance…
  • Step 3 Select One or more samples, each in a column from the drop-down menu, then click in the box below the drop-down menu and select C1.
  • Step 4 Click Options, choose the confidence level, click OK, then OK again. The confidence intervals for σ and σ2 are reported in the output, as shown in Figure 43.

SPSS

Finding the Critical Values and

  • Step 1 Enter a number in the first element of the first column.
  • Step 2 Click Transform > Compute Variable…
  • Step 3 To find : For Target Variable, provide the name of the first column. Under Function group, click Inverse DF. Under Functions and Special Variables, double-click Idf.Chisq. Replace the first question mark with “Enter the area to the left of” the desired critical value. For this will be (such as 0.025). Replace the second question mark with the degrees of freedom. Click OK twice.
  • Step 4 To find : Repeat Steps 1 and 2. For Target Variable, provide the name of the first column. Under Function group, click Inverse DF. Under Functions and Special Variables, double-click Idf.Chisq. Replace the first question mark with “Enter the area to the left of” the desired critical value. For this will be (such as 0.975). Replace the second question mark with the degrees of freedom. Click OK twice.

JMP

Finding the Critical Values and

  • Step 1 Click File > New > Data Table. Double-click the first element of Column 1. Right-click the header of Column 1 and click Column Info…, then from Column Properties select Formula and click Edit Formula.
  • Step 2 From Functions (grouped) select Probability, then click ChiSquare Quantile.
  • Step 3 To find : For p, enter the area to the left of the desired critical value. For this will be (such as 0.025). For DF, enter the degrees of freedom; see Figure 41. Click OK, then OK again.
  • Step 4 To find : Repeat Steps 1 and 2. For p, enter the area to the left of the desired critical value. For this will be (such as 0.975). For DF, enter the degrees of freedom. Click OK, then OK again.
  • Step 5 JMP displays the values of and in the column.

Finding a Confidence Interval for σ

  • Step 1 Input the data into Column 1. Name the column MPG.
  • Step 2 Select Analyze > Distribution. Select MPG and click Y, Columns. Click OK.
  • Step 3 Click the red triangle beside MPG, highlight Confidence Interval, and select 0.95. The second row of the Confidence Intervals table, shown in Figure 44, gives the 95% confidence interval for population standard deviation.
    image
    Figure 8.45: FIGURE 45 JMP Edit Formula for

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CRUNCHIT!

Finding the Critical Values and

  • Step 1 Click Distribution Calculator and select Chi-square.
  • Step 2 For df enter the degrees of freedom (such as 4).
  • Step 3 Select the Quantile tab. Enter the area (such as 0.025 for a 95% confidence interval). Click Calculate. CrunchIt! displays the value of .
  • Step 4 Enter the area (such as 0.975 for a 95% confidence interval). Click Calculate. CrunchIt! displays the value of