Confidence Intervals on the Casio fx-9750GII

Choose the interval before opening its menu

The fx-9750GII distinguishes a one-sample Z interval for a population mean with known population SD from a one-sample t interval when that SD is unknown. It also offers separate proportion and two-sample interval choices. Start with the parameter your problem asks about, then determine where its uncertainty estimate comes from. Selecting an interval because its input screen happens to accept your numbers can produce a plausible-looking answer for the wrong statistical method.

Open the one-sample normal interval

From the statistical data-list screen in STAT mode, follow the on-screen INTR, Z and 1-S labels for a one-sample Z interval. Use the parameter-data option when you have summary statistics rather than a raw list. Supply the confidence level, known population standard deviation, sample mean and sample count in the corresponding fields. Casio's manual describes both list and parameter specifications; a list supplies sample values but does not make the population SD known automatically.

Check a 95 percent worked example

For mean 50, known population SD 10 and n=100, use C-Level 0.95. The standard error is one, so the interval is about 48.040036 to 51.959964 when the more precise normal quantile is used. The local form uses z=1.96 and displays 48.04 to 51.96, agreeing at that precision. Compare the endpoints and method rather than requiring every final digit to match a different implementation's rounded critical value.

Interpret the confidence-level entry carefully

The manual states that values between zero and one represent the confidence proportion directly, while values from one up to but below 100 are divided by 100. Entering 0.95 avoids ambiguity for a 95% interval. Do not enter 0.05 when you mean 95% confidence; that is the total significance level, not the requested central coverage. After setting the parameters, move to Execute and use the displayed CALC command. The manual notes that these confidence-interval functions do not have a graph display.

Switch to t when the spread is estimated

For an unknown population SD, return to the interval menu and select t followed by 1-S. Supply the sample SD and sample count for parameter input, or the appropriate data list when using raw observations. A small example with observations 18, 20, 22, 24, 26 has mean 22, sample SD √10 and n=5. A 95% t interval uses four degrees of freedom and is approximately 18.073514 to 25.926486. The local normal-only form cannot verify that t interval simply by copying the same fields.

Check a second known-SD example

Use mean 20, known population SD 4 and n=25 at 95% confidence. The standard error is 0.8, and the device's normal-quantile interval is approximately 18.432029 to 21.567971. The local rounded-z check gives 18.432 to 21.568. If four is a sample SD instead, use the t workflow; with 24 degrees of freedom its interval is about 18.3489 to 21.6511. The wider result reflects the unknown-spread model, not a calculator fault.

Keep proportion and two-sample operations separate

For a success count and trial count, the device has a 1-Prop Z Interval choice under the Z interval menu. Its formula is a normal-approximation proportion interval, not a Wilson score interval. Small or extreme counts can require a more suitable method. A difference between two means or two proportions likewise needs its corresponding two-sample operation and assumptions. Do not subtract endpoints from two unrelated one-sample intervals and call the result a valid confidence interval for their difference.

Record the settings that make the answer reproducible

Write down the model name, selected interval type, confidence level, input values, data-list or parameter mode and final endpoints. Check that a raw-data frequency list represents actual counts rather than another measured variable. The navigation here follows the cited fx-9750GII software guide; it is not a claim that other Casio models share every menu. The device can calculate an interval correctly while the statistical assumptions fail, so retain the sampling context and justify the Z, t or proportion choice in the report.

Related guides

Find a 95% Confidence Interval for a Population Mean

Choose z or t from the source of the standard deviation, compute two 95% mean intervals, and check sampling assumptions and interpretation.

Find a Confidence Interval When SD Is Missing

Determine whether raw data, variance, standard error or a previous interval supplies the missing spread, and know when a mean interval is underdetermined.

Confidence Interval Formula for a Population Proportion

Compute a sample proportion, compare Wald and Wilson intervals, and handle zero successes without claiming zero population uncertainty.