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:
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.
