How to find a confidence interval for a mean on the Casio fx-CG50
t and z confidence intervals for a population mean, from a list of data or from summary statistics. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
Confidence intervals are in Further Statistics (and IAL S3) rather than A Level Maths.
Practise it: Hypothesis testing.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Confidence intervals on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- MENU 2, data in List 1.
- t-interval: F4 (INTR) F2 (t) F1 (1-SAMPLE). Data: List, C-Level 0.95, List: List1, Freq 1. Execute. Read Left and Right.
- z-interval (σ known): F4 (INTR) F1 (Z) F1 (1-SAMPLE), C-Level 0.95, σ 0.3, List1. Execute.
- From summary statistics: choose Data: Variable and type x̄, sx (or σ) and n instead of a list.
- C-Level is a decimal (0.95), not 95.
Confidence intervals on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- Data in L1. stat → TESTS → 8: TInterval. Inpt: Data, List L1, Freq 1, C-Level 0.95. Calculate.
- σ known: 7: ZInterval, σ 0.3.
- Summary statistics: Inpt: Stats and type x̄, Sx and n.
Confidence intervals on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Data in a named list. menu → Statistics → Confidence Intervals → t Interval → Data. Choose the list, C Level 0.95. OK.
- σ known: z Interval.
- The results are stored as stat.CLower and stat.CUpper.
Confidence intervals on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
The fx-991EX has no confidence-interval function and no t-distribution. With σ known you can build a z-interval by hand: x̄ ± z × σ ÷ √n, with z from Inverse Normal (Area 0.975, σ 1, μ 0) = 1.95996.
Confidence intervals on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
The fx-991CW has no confidence-interval function. For σ known use x̄ ± z × σ ÷ √n with z from Inverse Normal (Area 0.975).
Worked example
Masses (kg): 4.2, 3.9, 4.5, 4.1, 3.8, 4.4, 4.0, 4.3, 3.7, 4.6. (a) Find a 95% confidence interval for the mean. (b) The same, if σ = 0.3 is known.
Answers (checked with Python)
x̄ = 4.15, s = 0.302765. (a) t-interval: (3.93341, 4.36659). (b) z-interval: (3.96406, 4.33594).
Common calculator mistakes
- Using a z-interval when σ is unknown and estimated from the sample (use t).
- Typing 95 instead of 0.95 for the level.
- Giving the interval without interpreting it: "we are 95% confident the population mean lies between 3.93 and 4.37 kg".
- Using σ where the question gives a sample standard deviation, or dividing by n instead of √n.
Do it in Desmos
Not in the exam. Desmos is not allowed in A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- Make a list M of the data.
- tinterval(M) gives the t-interval; its menu sets the confidence level.
- Check by hand: mean(M) ± tdist(9).inversecdf(0.975) × stdev(M)/√10.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
M=[4.2,3.9,4.5,4.1,3.8,4.4,4,4.3,3.7,4.6]tinterval(M)mean(M)-tdist(9).inversecdf(0.975)·frac{stdev(M)}{√{10}}
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.