Confidence Intervals on TI-84 Calculator

Confidence Intervals on TI-84 Calculator, A confidence interval (C.I.) is a statistical tool that provides a range of values, likely to contain a population parameter with a specified level of confidence.

Confidence Intervals on TI-84 Calculator

This guide walks you through the process of calculating various confidence intervals using a TI-84 calculator, specifically:

1. Confidence interval for a population mean when the population standard deviation (σ) is known.
2. Confidence interval for a population mean when σ is unknown.
3. Confidence interval for a population proportion.

Example 1: Confidence Interval for a Population Mean; σ Known

Objective: Calculate a 95% confidence interval for a population mean with the following details:

• Sample Mean (x̄) = 14
• Sample Size (n) = 35
• Population Standard Deviation (σ) = 4

Step 1: Select the Z Interval.

1. Press the STAT button.
2. Navigate to TESTS.
3. Highlight 7: ZInterval and press ENTER.

Step 2: Enter Required Information.

The calculator prompts you to provide:

• Input Type: Choose Stats and then press ENTER.
• σ: Enter the population standard deviation as 4 and press ENTER.
• x̄: Input the sample mean 14 and press ENTER.
• n: Input the sample size 35 and press ENTER.
• C-level: Enter the confidence level 0.95 and press ENTER.

Finally, highlight Calculate and press ENTER again.

Step 3: Interpret the Results.

After pressing ENTER, the calculator displays the 95% confidence interval for the population mean:
(12.675, 15.325).

Example 2: Confidence Interval for a Population Mean; σ Unknown

Objective: Calculate a 95% confidence interval for a population mean with the following details:

• Sample Mean (x̄) = 12
• Sample Size (n) = 19
• Sample Standard Deviation (Sx) = 6.3

Step 1: Select the T Interval.

1. Press the STAT button.
2. Navigate to TESTS.
3. Highlight 8: TInterval and press ENTER.

Step 2: Enter Required Information.

The calculator prompts you to provide:

• Input Type: Choose Stats and then press ENTER.
• x̄: Input the sample mean 12 and press ENTER.
• Sx: Enter the sample standard deviation as 6.3 and press ENTER.
• n: Input the sample size 19 and press ENTER.
• C-level: Enter the confidence level 0.95 and press ENTER.

Finally, highlight Calculate and press ENTER again.

Step 3: Interpret the Results.

After pressing ENTER, the calculator displays the 95% confidence interval for the population mean:
(8.9635, 15.037).

Example 3: Confidence Interval for a Population Proportion

Objective: Calculate a 95% confidence interval for a population proportion with the following details:

• Number of “successes” (x) = 12
• Number of trials (n) = 19

Step 1: Select the 1-Proportion Z Interval.

1. Press the STAT button.
2. Navigate to TESTS.
3. Highlight 1-PropZInt and press ENTER.

Step 2: Enter Required Information.

The calculator prompts you to provide:

• x: Input the number of successes 12 and press ENTER.
• n: Input the number of trials 19 and press ENTER.
• C-level: Enter the confidence level 0.95 and press ENTER.

Finally, highlight Calculate and press ENTER again.

Step 3: Interpret the Results.

After pressing ENTER, the calculator displays the 95% confidence interval for the population proportion:
(0.41468, 0.84848).

Conclusion

Confidence intervals are a vital part of statistical analysis, providing important insights into population parameters based on sample data.

The TI-84 calculator simplifies these calculations, making it easier for users to interpret their data with confidence.

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