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Casio fx-CG50 field manual for IB Math

AI HL only · 41 of 44

41

One-sample t-test from data

AI HL

Enter raw data into a list and run a one-sample t-test on it, letting the calculator find xˉ and sx​ before reading t and the p-value.

Goal

Test ​H0​:μ=12​ against ​Ha​:μ<12​ using the sample ​11.6,  ​12.3,  ​11.4,  ​11.9,  ​12.1,  ​11.2,  ​11.8,  ​11.5,  ​12.0,  ​11.7.

1

From the MAIN MENU, open Statistics. If you're already inside another app, press first to get back to MAIN MENU.

2

Type the ten values down List 1, pressing after each one.

RadNorm2
d/cReal
List 1List 2List 3List 4SUB111.6212.3311.4411.9512.1611.2711.8811.59121011.7
GRAPHCALCTESTINTRDIST▷
3

Press (TEST), then (t), then (1-SAMPLE).

4

With the cursor on Data, press (List) so the test reads the sample instead of asking for summary statistics. Set the alternative μ to <μ0, enter μ0 = 12, set List to List 1, and leave Freq at 1. The calculator works out ​xˉ​ and ​sx​ from the list.

RadNorm2
d/cReal
1-Sample tTest
Data:List
μ:<μ0
μ0:12
List:List 1
Freq:1
Save Res:None
↓
CALCDRAW
5

Move down to Execute and press (CALC).

Result

​t≈−2.34​ and ​p≈0.0219, so at the 5% level there is sufficient evidence to reject ​H0​.

RadNorm2
d/cReal
1-Sample tTest
μ<12
t=-2.3426064
p=0.02191638
x̄=11.75
sx=0.33747428
n=10

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Test ​H0​:μ=30​ against ​Ha​:μ<30​ using the sample ​29.6,  ​28.9,  ​30.4,  ​28.4,  ​30.1,  ​29.3,  ​30.2,  ​28.6, at the 5% level.

  2. 2

    Test ​H0​:μ=8​ against ​Ha​:μ<8​ using the sample ​7.9,  ​8.2,  ​7.6,  ​8.0,  ​7.7,  ​8.1,  ​7.5,  ​7.8,  ​8.3,  ​7.6,  ​7.9,  ​7.7, at the 5% level.

  3. 3

    Test ​H0​:μ=120​ against ​Ha​:μ<120​ using the sample ​118,  ​122,  ​116,  ​119,  ​117,  ​123,  ​118,  ​115,  ​121,  ​117, at the 5% level.