CAS calculators (TI-Nspire, Casio ClassPad) have built-in statistical inference functions. They compute test statistics, p-values, and confidence intervals accurately without manual table look-up, reducing calculation errors.
TI-Nspire:
- For a mean (known $\sigma$): Stats → Confidence Intervals → z Interval
- Input: $\bar{x}$, $\sigma$ (population), $n$, confidence level (e.g. 0.95)
- Output: lower bound, upper bound, margin of error
For a proportion:
- Stats → Confidence Intervals → 1-Prop z Interval
- Input: $x$ (successes), $n$, confidence level
z-test for mean:
- Stats → Hypothesis Tests → z Test
- Input: $\mu_0$ (null value), $\bar{x}$, $\sigma$, $n$, tail (left/right/two)
- Output: test statistic $z$, p-value, decision
1-proportion z-test:
- Stats → Hypothesis Tests → 1-Prop z Test
- Input: $p_0$, $x$ (successes), $n$, alternative
Sample data: $\bar{x} = 23.4$, $\sigma = 4.2$, $n = 50$, confidence level 95%.
Enter into z Interval. CAS returns: $(22.24,\; 24.56)$.
Interpretation: “We are 95% confident the true population mean is between 22.24 and 24.56.”
Always verify a CAS result for a simple case:
$$\text{Margin of error} = 1.96 \times \frac{4.2}{\sqrt{50}} = 1.96 \times 0.594 = 1.164$$
$$\text{CI} = 23.4 \pm 1.164 = (22.236,\; 24.564) \quad \checkmark$$
CAS outputs:
- Test statistic $z$: how many standard errors the sample statistic is from $H_0$
- p-value: compare to $\alpha$; if $p < \alpha$, reject $H_0$
| CAS output | Meaning |
|---|---|
| $z = -2.34$ | Sample mean is 2.34 SEs below $H_0$ value |
| $p = 0.019$ | 1.9% chance of this result if $H_0$ were true |
| Reject $H_0$ at $\alpha = 0.05$ | Evidence against the null hypothesis |
STUDY HINT: Practise navigating to inference menus on your CAS before the exam. Know whether to enter raw counts or proportions for 1-proportion tests.
EXAM TIP: CAS output alone is insufficient for full marks. Write down what you entered, the output values, and a contextual conclusion sentence.
