Dawnbridge

TI-84 Plus CE 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 the list editor with → 1: Edit and enter the data values in L1.

NORMALFLOATAUTOREALRADIANMP
L1L2L3L4L511.6------------------------12.311.411.912.111.211.811.512
2

Press , move right to TESTS, and choose 2: T-Test.

3

Set Inpt to Data (you have the raw data, not summary statistics). Enter μ0: 12, set List to L1 (typed with ), leave Freq: 1, and select the alternative ​μ<μ0​. The calculator finds ​xˉ​ and ​Sx​​ from the list itself. If you only had summary statistics, you would set Inpt to Stats and type them in instead.

NORMALFLOATAUTOREALRADIANMP
T-Test
Inpt:DataStats
μ₀:12
List:L1
Freq:1
μ:≠μ₀<μ₀>μ₀
Color:BLUE
CalculateDraw
4

Move down to Calculate and press .

Result

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

NORMALFLOATAUTOREALRADIANMP
T-Test
μ<12
t=-2.342606428
p=0.0219163756
x̄=11.75
Sx=0.3374742789
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.