Matched pairs (dependent) 2 samples

9.3   
t-Test and t-Interval

Visualize 2 dependent samples

In the Visualizer:
Use the "Cholesterol before and after heart attack" data.
270 236 210 142 280 272 160 220 226 242 186 266 206 318 294 282 234 224 276 282 360 310 280 278 288 288 244 236
218 234 214 116 200 276 146 182 238 288 190 236 244 258 240 294 220 200 220 186 352 202 218 248 278 248 270 242

n=____
X1 mean=______     X2 mean=_______
X1 SD  =______     X2 SD  =_______

Does it look like cholesterol increased, decreased, or stayed the same:________
(i.e. more red: decrease, more black: increase)

mean of the paired differences d̄=_______
X1 mean - X2 mean =_______


Paste the data into the "t-Test and t-Interval" webpage.
Do a Two-tailed hypothesis test that the means are different. Ha≠H0

t=______    
Critical value .05=______   Reject H0?:_____
Critical value .01=______   Reject H0?:_____

p-value=_______
 Reject H0 at α=.05?:_____
 Reject H0 at α=.01?:_____

95% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___
99% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___


************************************************************

In the Visualizer:
Use the "hypnotism" data.
6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6
6.8 2.4 7.4  8.5  8.1 6.1 3.4  2.0

n=____
X1 mean=______     X2 mean=_______
X1 SD  =______     X2 SD  =_______

Does it look like the data increased, decreased, or stayed the same:________
(i.e. more red: decrease, more black: increase)

mean of the paired differences d̄=_______
X1 mean - X2 mean =_______


Paste the data into the "t-Test and t-Interval" webpage.
Do a Two-tailed hypothesis test that the means are different. Ha≠H0

t=______    
Critical value α=.05=______   Reject H0?:_____
Critical value α=.01=______   Reject H0?:_____

p-value=_______
Reject H0 at α=.05?:_____
Reject H0 at α=.01?:_____

95% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___
99% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___

Look at the Visualizer again, it's all red but that one black line of increase 
is preventing rejecting H0 at the 99% CL.


************************************************************

In the Visualizer:
Use the "Banks' deposits. 3 years ago and now" data..
11.42 8.41 3.98 7.37 2.28 1.10 1.00 0.9 1.35
16.69 9.44 6.53 5.58 2.92 1.88 1.78 1.5 1.22

n=____
X1 mean=______     X2 mean=_______
X1 SD  =______     X2 SD  =_______

Does it look like the bank deposits increased, decreased, or stayed the same:________
(i.e. more red: decrease, more black: increase)

mean of the paired differences d̄=_______
X1 mean - X2 mean =_______


Paste the data into the "t-Test and t-Interval" webpage.
Do a Two-tailed hypothesis test that the means are different. Ha≠H0

t=______    
Critical value α=.05=______   Reject H0?:_____
Critical value α=.01=______   Reject H0?:_____

p-value=_______
Reject H0 at α=.05?:_____
Reject H0 at α=.01?:_____

95% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___
99% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___

Most of the increases were tiny, so no statically significant difference.

************************************************************

In the Visualizer:
Use the "Banks modified" data..
11.42  8.41 3.98 7.37 2.28 1.10 1.00 0.9 1.35
16.69 12.44 6.53 5.58 4.92 3.88 0.9  1.5 1.22

n=____
X1 mean=______     X2 mean=_______
X1 SD  =______     X2 SD  =_______

Does it look like the Bonus data increased, decreased, or stayed the same:________
(i.e. more red: decrease, more black: increase)

mean of the paired differences d̄=_______
X1 mean - X2 mean =_______

What statistics are different from the previous Banks data above:______________

Paste the data into the "t-Test and t-Interval" webpage.
Do a Two-tailed hypothesis test that the means are different. Ha≠H0

t=______    
Critical value α=.05=______   Reject H0?:_____
Critical value α=.01=______   Reject H0?:_____

p-value=_______
Reject H0 at α=.05?:_____
Reject H0 at α=.01?:_____

95% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___
99% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___



************************************************************

In the Visualizer:
Use the "Bonus 2" data..
122 102 115 109 93 97 85 102 106 98 112 76 90 113 110 121 99 93 108 82 
128 96 117 115 98 94 79 109 120 104 83 81 88 139 116 139 113 97 114 84

n=____
X1 mean=______     X2 mean=_______
X1 SD  =______     X2 SD  =_______

Does it look like the Bonus data increased, decreased, or stayed the same:________
(i.e. more red: decrease, more black: increase)

mean of the paired differences d̄=_______
X1 mean - X2 mean =_______


Paste the data into the "t-Test and t-Interval" webpage.
Do a Two-tailed hypothesis test that the means are different. Ha≠H0

t=______    
Critical value α=.05=______   Reject H0?:_____
Critical value α=.01=______   Reject H0?:_____

p-value=_______
Reject H0 at α=.05?:_____
Reject H0 at α=.01?:_____

95% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___
99% CL: E=_____   CI:[_____,______]   Contains 0?:____  Reject H0?:___

A mix of increases and decreases tends not to be statistically significant.