STEP-BY-STEP TECHNOLOGY GUIDE: Z Confidence Intervals

We illustrate how to construct the confidence interval for Example 6 (page 436).

TI-83/84

If you have the data values:

  • Step 1 Enter the data into list L1 (Figure 10).
  • Step 2 Press STAT, highlight TESTS.
  • Step 3 Press 7 (for ZInterval).

  • Step 4 For input (Inpt), highlight Data and press ENTER (Figure 11).

    1. For σ, enter the assumed value of 6.326.
    2. For List, press 2nd then L1.
    3. For Freq, enter 1.
    4. For C-Level (confidence level), enter the appropriate confidence level (e.g., 0.95), and press ENTER.
    5. Highlight Calculate and press ENTER. The results are shown in Figure 5 in Example 6.

If you have the summary statistics:

  • Step 1 Press STAT, and highlight TESTS.
  • Step 2 Press 7 (for ZInterval).
  • Step 3 For input (Inpt), highlight Stats and press ENTER (Figure 12).
    1. For σ, enter the assumed value of 6.326.
    2. For x̄, enter the sample mean 26.9375.
    3. For n, enter the sample size 16 .
    4. For C-Level (confidence level), enter the appropriate confidence level (e.g., 0.95), and press ENTER.
    5. Highlight Calculate and press ENTER. The results are shown in Figure 5 in Example 6.
      image
      Figure 8.10: FIGURE 10
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      Figure 8.11: FIGURE 11
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      Figure 8.12: FIGURE 12

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EXCEL

If you have the data values:

  • Step 1 Enter the data into Column A.
  • Step 2 Label C1 through F1 X-bar, Std Err, X-bar – StdErr, and X-bar + Std Err.
  • Step 3 In cell C2, type = AVERAGE (A1: A16) . Press ENTER.

  • Step 4 Click cell D2, and click the Insert Function icon fx.

    Under Search for a function, type confidence.norm. Click Go, and OK.

  • Step 5 Enter the Alpha value, 0.05, the known standard deviation (Standard_dev) 6.326, and the sample Size 16 . Click OK.
  • Step 6 In cell E2, type =C2−D2, and press ENTER. In cell F2, type =C2+D2, and press ENTER. Cells E2 and F2 are your confidence interval. Results are shown in Figure 13.

If you have the summary statistics:

  • Step 1 Label C1 through F1 X-bar, Std Err, X-bar – StdErr, and X-bar + StdErr.
  • Step 2 In cell C2, enter the sample average 26.9375.
    image
    Figure 8.13: FIGURE 13 Excel results.
  • Step 3 Click cell D2, and click the Insert Function icon fx. Under Search for a function, type confidence.norm. Click Go, and OK.
  • Step 4 Enter the Alpha value, 0.05, the known standard deviation (Standard_dev) 6.326, and the sample Size 16. Click OK.
  • Step 5 In cell E2, type =C2−D2, and press ENTER. In cell F2, type =C2+D2, and press ENTER. Cells E2 and F2 are your confidence interval.

MINITAB

If you have the data values:

  • Step 1 Enter the data into column C1.
  • Step 2 Click Stat > Basic Statistics > 1-Sample Z…
  • Step 3 Select One or more samples, each in a column from the drop-down menu. Click in the empty box below the menu, click C1, then click Select.
  • Step 4 Click Options…, enter 95 as the confidence Level, and click OK.
  • Step 5 Enter 6.326 for Known standard deviation and click OK.

The results are displayed in Figure 6 in Example 6.

If you have the summary statistics:

  • Step 1 Click Stat > Basic Statistics > 1-Sample Z…
  • Step 2 Click Summarized Data from the drop-down menu.
  • Step 3 Enter the Sample size, 16, and the Sample mean, 26.9375.
  • Step 4 Enter 6.326 for the Known standard deviation.
  • Step 5 Click Options…, enter 95.0 as the confidence level, click OK, and click OK again.

JMP

If you have the data values:

  • Step 1 Click File > New > Data Table. Enter the data into Column 1.
  • Step 2 Click Analyze > Distribution. Click Column 1 under Select Columns, then click Y, Columns. Click OK.
  • Step 3 Click the red triangle beside Column 1, and click confidence Interval, then Other…
  • Step 4 For Enter (1-alpha) for confidence interval, enter 0.95, select Two-sided and click Use known Sigma. Click OK.
  • Step 5 For Enter known Sigma, enter 6.326 and click OK. The output is shown in Figure 7.

CRUNCHIT!

If you have the data values:

  • Step 1 Click File, then highlight Load from Larose, Discostat3e > Chapter 8, and click on Example 01_06.
  • Step 2 Click Statistics > z and select 1-sample.
  • Step 3 With the Columns tab chosen, for Sample select Highway MPG. For Standard Deviation, enter 6.326.
  • Step 4 Select the confidence Interval tab, and enter 95 for the confidence Interval Level (%). Then click Calculate.

If you have the summary statistics:

  • Step 1 Click Statistics > z and select 1-sample.
  • Step 2 Choose the Summarized tab. For n, enter the sample size 16; for Sample Mean, enter 26.9375. For Standard Deviation, enter 6.326.
  • Step 3 Select the confidence Interval tab, and enter 95 for the confidence Interval Level (%). Then click Calculate.