Dawnbridge

TI-Nspire CX II field manual for IB Math

AI HL only · 42 of 45

42

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

Open a Lists & Spreadsheet page, name the first column data, and enter the values.

*Document
RAD
AdataBCD=111.6212.3311.4411.9512.1A1
2

Still on the Lists & Spreadsheet page, press → Statistics → Stat Tests → 2: t Test. Set Data Input Method to Data. If you only had summary statistics, you would choose Stats here and type them in instead.

3

Fill in the dialog, moving between fields with : μ0: 12, set List to the named column data, leave Frequency List: 1, and set Alternate Hyp to ​Ha​:μ<μ0​. The Nspire computes ​xˉ​ and ​sx​​ from the list itself.

*Document
RAD
t Test
μ0:12▶
List:data▶
Frequency List:1▶
Alternate Hyp:Ha: μ < μ0▶
1st Result Columnc[]▶
OKCancel
4

Select OK and press . The result labels and values paste straight into the spreadsheet.

Result

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

*Document
RAD
tTest 12,data,1.,−1:stat.results
⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡​”Title””Alternate Hyp””t””PVal””df””x̄””sx := sn-1x””n”​”t Test””μ < μ0”−2.342610.02191649.11.750.33747410.​⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤​

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.