The data was first tested to see if there was a difference between smokers and non
smokers. A two sample t test was conducted with an alpha of 0.05.
H0: µ1= µ2 Ha: µ1≠ µ2
With a P-value greater than 0.05 in can be concluded that the means are equal (that the
original hypothesis is true). Below is the output for this hypothesis test for each question
for each group.
Two-sample T for A Q1
Smoker?
0
1
N
24
24
Mean
3.58
3.17
StDev
1.06
1.43
SE Mean
0.22
0.29
Difference = mu (0) - mu (1)
Estimate for difference: 0.417
90% lower bound for difference: -0.057
T-Test of difference = 0.5 (vs >): T-Value = -0.23
P-Value = 0.590
DF = 42
P-Value = 0.655
DF = 43
Accept Null… NO difference
Two-sample T for A Q2
Smoker?
0
1
N
24
22
Mean
2.63
2.27
StDev
1.21
1.28
SE Mean
0.25
0.27
Difference = mu (0) - mu (1)
Estimate for difference: 0.352
90% lower bound for difference: -0.126
T-Test of difference = 0.5 (vs >): T-Value = -0.40
Accept Null… NO Difference
Two-sample T for A Q3
Smoker?
0
1
N
24
24
Mean
2.96
2.25
StDev
1.52
1.39
SE Mean
0.31
0.28
Difference = mu (0) - mu (1)
Estimate for difference: 0.708
90% lower bound for difference: 0.162
T-Test of difference = 0.5 (vs >): T-Value = 0.50
Accept Null.. No Difference
Two-sample T for B Q1
Smoker?
0
1
N
24
24
Mean
2.46
2.17
StDev
1.28
1.17
SE Mean
0.26
0.24
Difference = mu (0) - mu (1)
P-Value = 0.311
DF = 45
Estimate for difference: 0.292
90% lower bound for difference: -0.169
T-Test of difference = 0.5 (vs >): T-Value = -0.59
P-Value = 0.720
DF = 45
P-Value = 0.597
DF = 44
Accept Null… No Difference
Two-sample T for B Q2
Smoker?
0
1
N
24
23
Mean
2.54
2.13
StDev
1.22
1.25
SE Mean
0.25
0.26
Difference = mu (0) - mu (1)
Estimate for difference: 0.411
90% lower bound for difference: -0.058
T-Test of difference = 0.5 (vs >): T-Value = -0.25
Accept Null… No Difference
Two-sample T for B Q3
Smoker?
0
1
N
24
23
Mean
2.63
2.00
StDev
1.06
1.35
SE Mean
0.22
0.28
Difference = mu (0) - mu (1)
Estimate for difference: 0.625
90% lower bound for difference: 0.164
T-Test of difference = 0.5 (vs >): T-Value = 0.35
P-Value = 0.363
DF = 41
Accept Null… No Difference
Two-sample T for C Q1
Smoker?
0
1
N
23
24
Mean
3.57
3.42
StDev
1.16
1.14
SE Mean
0.24
0.23
Difference = mu (0) - mu (1)
Estimate for difference: 0.149
90% lower bound for difference: -0.288
T-Test of difference = 0.5 (vs >): T-Value = -1.05
P-Value = 0.850
DF = 44
P-Value = 0.799
DF = 43
Accept Null… No Difference
Two-sample T for C Q2
Smoker?
0
1
N
23
23
Mean
3.65
3.48
StDev
1.27
1.34
SE Mean
0.26
0.28
Difference = mu (0) - mu (1)
Estimate for difference: 0.174
90% lower bound for difference: -0.327
T-Test of difference = 0.5 (vs >): T-Value = -0.85
Accept Null… No Difference
Two-sample T for C Q3
Smoker?
0
1
N
23
24
Mean
3.39
2.96
StDev
1.27
1.40
SE Mean
0.26
0.29
Difference = mu (0) - mu (1)
Estimate for difference: 0.433
90% lower bound for difference: -0.074
T-Test of difference = 0.5 (vs >): T-Value = -0.17
P-Value = 0.568
DF = 44
P-Value = 0.971
DF = 40
P-Value = 0.825
DF = 43
P-Value = 0.717
DF = 44
Accept Null… No Difference
Two-sample T for D Q1
Smoker?
0
1
N
23
22
Mean
2.652
2.73
StDev
0.885
1.08
SE Mean
0.18
0.23
Difference = mu (0) - mu (1)
Estimate for difference: -0.075
90% lower bound for difference: -0.459
T-Test of difference = 0.5 (vs >): T-Value = -1.95
Accept Null… No Difference
Two-sample T for D Q2
Smoker?
0
1
N
24
22
Mean
2.92
2.77
StDev
1.28
1.27
SE Mean
0.26
0.27
Difference = mu (0) - mu (1)
Estimate for difference: 0.144
90% lower bound for difference: -0.346
T-Test of difference = 0.5 (vs >): T-Value = -0.95
Accept Null… No Difference
Two-sample T for D Q3
Smoker?
0
1
N
24
24
Mean
2.83
2.54
StDev
1.13
1.35
SE Mean
0.23
0.28
Difference = mu (0) - mu (1)
Estimate for difference: 0.292
90% lower bound for difference: -0.176
T-Test of difference = 0.5 (vs >): T-Value = -0.58
Accept Null.. No Difference
Two-sample T for E Q1
Smoker?
0
1
N
24
24
Mean
3.08
2.583
StDev
1.21
0.929
SE Mean
0.25
0.19
Difference = mu (0) - mu (1)
Estimate for difference: 0.500
90% lower bound for difference: 0.094
T-Test of difference = 0.5 (vs >): T-Value = 0.00
P-Value = 0.500
DF = 43
P-Value = 0.154
DF = 40
P-Value = 0.249
DF = 44
Accept Null… No Difference
Two-sample T for E Q2
Smoker?
0
1
N
24
23
Mean
3.583
2.74
StDev
0.974
1.29
SE Mean
0.20
0.27
Difference = mu (0) - mu (1)
Estimate for difference: 0.844
90% lower bound for difference: 0.409
T-Test of difference = 0.5 (vs >): T-Value = 1.03
Accept Null… no difference
Two-sample T for E Q3
Smoker?
0
1
N
24
23
Mean
3.33
2.61
StDev
1.09
1.16
SE Mean
0.22
0.24
Difference = mu (0) - mu (1)
Estimate for difference: 0.725
90% lower bound for difference: 0.298
T-Test of difference = 0.5 (vs >): T-Value = 0.68
Accept Null… No difference
Two-sample T for F Q1
Smoker?
0
1
N
24
24
Mean
2.500
3.08
StDev
0.885
1.28
SE Mean
0.18
0.26
Difference = mu (0) - mu (1)
Estimate for difference: -0.583
90% lower bound for difference: -0.998
T-Test of difference = 0.5 (vs >): T-Value = -3.41
P-Value = 0.999
DF = 40
P-Value = 0.988
DF = 40
Two-sample T for F Q2
Smoker?
0
1
N
24
23
Mean
2.79
3.13
StDev
1.02
1.39
SE Mean
0.21
0.29
Difference = mu (0) - mu (1)
Estimate for difference: -0.339
90% lower bound for difference: -0.804
T-Test of difference = 0.5 (vs >): T-Value = -2.35
Accept Null… No Difference
Two-sample T for F Q3
Smoker?
0
1
N
24
23
Mean
3.08
2.35
StDev
1.28
1.37
SE Mean
0.26
0.29
Difference = mu (0) - mu (1)
Estimate for difference: 0.736
90% lower bound for difference: 0.232
T-Test of difference = 0.5 (vs >): T-Value = 0.61
P-Value = 0.273
DF = 44
Accept Null… No Difference in mean
After there was proven to be no statistical difference between non-smokers and smokers,
the descriptive statistics for each question in every group were calculated in Minitab. The
output is seen below.
Descriptive Statistics: A Q1, A Q2, A Q3, B Q1, B Q2, B Q3, C Q1, C Q2, ...
Variable
A Q1
A Q2
A Q3
B Q1
B Q2
B Q3
C Q1
C Q2
C Q3
D Q1
D Q2
D Q3
E Q1
E Q2
E Q3
F Q1
F Q2
F Q3
N
48
46
48
48
47
47
47
46
47
45
46
48
48
47
47
48
47
47
N*
0
2
0
0
1
1
1
2
1
3
2
0
0
1
1
0
1
1
Mean
3.375
2.457
2.604
2.313
2.340
2.319
3.489
3.565
3.170
2.689
2.848
2.688
2.833
3.170
2.979
2.792
2.957
2.723
SE Mean
0.183
0.183
0.214
0.177
0.181
0.180
0.166
0.191
0.196
0.145
0.186
0.179
0.158
0.176
0.171
0.163
0.177
0.199
StDev
1.265
1.242
1.484
1.223
1.238
1.235
1.140
1.294
1.340
0.973
1.264
1.240
1.098
1.204
1.170
1.129
1.215
1.363
Minimum
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Q1
2.000
1.750
1.000
1.000
1.000
1.000
3.000
3.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
1.000
Median
3.500
2.000
2.000
2.000
2.000
2.000
4.000
4.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
Q3
4.000
4.000
4.000
3.000
3.000
3.000
4.000
5.000
4.000
3.500
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
Maximum
5.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
4.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
Each question could now be evaluated to conclude if the average response was <, =, or >
3. The number 3 was tested because 3 is the neutral response for each question, which
was explained to participants when the survey was given to them. This was tested with a
1 sample Z test. With the conclusion to this hypothesis test the families were given a
score for each question. If the mean was proven to be less than 3 it received a score of 1.
If the mean was proven to be equal to 3 it received a score of 3. Lastly if the mean was
proven to be greater than 3 it received a score of 5.
Ha: µ1 < 3, µ1≠ 3, µ1> 3
α= 0.05
The results to each of the hypothesis tests can be seen below. Histograms were also made
for each of the tests to visually show the conclusion to the hypothesis test. The histogram
H0: 3= µ1
can be read as follows: The red point is the mean value that as tested, the blue line is the
mean with a confidence interval of 95% for the test. If the blue line goes through the red
point then the mean equals 3. If the blue line if all greater than 3 (to the right of the red
point) than the mean is greater than 3 and if it is to the left of the red point the mean is
less than 3.
One-Sample Z: A Q1
Test of mu = 3 vs > 3
The assumed standard deviation = 1.265
Variable
A Q1
N
48
Mean
3.375
StDev
1.265
SE Mean
0.183
95% Lower
Bound
3.075
Z
2.05
P
0.020
Reject The null… A Q1 is > 3
One-Sample Z: A Q2
Test of mu = 3 vs < 3
The assumed standard deviation = 1.242
Variable
A Q2
N
46
Mean
2.457
StDev
1.242
SE Mean
0.183
95% Upper
Bound
2.758
Z
-2.97
P
0.001
Reject the Null… A Q2 < 3
One-Sample Z: A Q3
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.484
Variable
A Q3
N
48
Mean
2.604
StDev
1.484
SE Mean
0.214
95% CI
(2.184, 3.024)
Z
-1.85
Accept Null…A Q3 = 3
One-Sample Z: B Q1
Test of mu = 3 vs < 3
The assumed standard deviation = 1.223
Variable
B Q1
N
48
Mean
2.313
StDev
1.223
SE Mean
0.177
95% Upper
Bound
2.603
REJECT NULL… B Q1 < 3
One-Sample Z: B Q2
Test of mu = 3 vs < 3
The assumed standard deviation = 1.238
Z
-3.89
P
0.000
P
0.065
Variable
B Q2
N
47
Mean
2.340
StDev
1.238
95% Upper
Bound
2.637
SE Mean
0.181
Z
-3.65
P
0.000
95% Upper
Bound
2.615
Z
-3.78
P
0.000
95% Lower
Bound
3.216
Z
2.94
P
0.002
Z
2.96
P
0.002
REJECT NULL… B Q2 < 3
One-Sample Z: B Q3
Test of mu = 3 vs < 3
The assumed standard deviation = 1.235
Variable
B Q3
N
47
Mean
2.319
StDev
1.235
SE Mean
0.180
REJECT NULL… B Q3 < 3
One-Sample Z: C Q1
Test of mu = 3 vs > 3
The assumed standard deviation = 1.14
Variable
C Q1
N
47
Mean
3.489
StDev
1.140
SE Mean
0.166
REJECT NULL… C Q1 >3
One-Sample Z: C Q2
Test of mu = 3 vs > 3
The assumed standard deviation = 1.294
Variable
C Q2
N
46
Mean
3.565
StDev
1.294
95% Lower
Bound
3.251
SE Mean
0.191
REJECT NULL… C Q2 >3
One-Sample Z: C Q3
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.34
Variable
C Q3
N
47
Mean
3.170
StDev
1.340
SE Mean
0.195
95% CI
(2.787, 3.553)
Z
0.87
P
0.384
REJECT NULL… C Q3 = 3
One-Sample Z: D Q1
Test of mu = 3 vs < 3
The assumed standard deviation = 0.973
Variable
D Q1
N
45
Mean
2.689
StDev
0.973
SE Mean
0.145
95% Upper
Bound
2.927
Z
-2.14
P
0.016
REJECT NULL… D Q1 < 3
One-Sample Z: D Q2
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.264
Variable
D Q2
N
46
Mean
2.848
StDev
1.264
SE Mean
0.186
95% CI
(2.483, 3.213)
Z
-0.82
P
0.414
95% CI
(2.337, 3.038)
Z
-1.75
P
0.081
Z
-1.05
P
0.293
ACCEPT NULL D Q2 = 3
One-Sample Z: D Q3
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.24
Variable
D Q3
N
48
Mean
2.688
StDev
1.240
SE Mean
0.179
ACCEPT NULL… D Q3 = 3
One-Sample Z: E Q1
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.098
Variable
E Q1
N
48
Mean
2.833
StDev
1.098
SE Mean
0.158
95% CI
(2.523, 3.144)
ACCEPT NULL E Q1 = 3
One-Sample Z: E Q2
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.204
Variable
E Q2
N
47
Mean
3.170
StDev
1.204
SE Mean
0.176
95% CI
(2.826, 3.514)
Z
0.97
95% CI
(2.644, 3.313)
Z
-0.12
P
0.332
ACCEPT NULL… E Q2 = 3
One-Sample Z: E Q3
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.17
Variable
E Q3
N
47
Mean
2.979
ACCEPT NULL… E Q3 = 3
StDev
1.170
One-Sample Z: F Q1
SE Mean
0.171
P
0.901
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.129
Variable
F Q1
N
48
Mean
2.792
StDev
1.129
SE Mean
0.163
95% CI
(2.472, 3.111)
Z
-1.28
P
0.201
Z
-0.24
P
0.810
Z
-1.39
P
0.166
ACCEPT NULL… F Q1 = 3
One-Sample Z: F Q2
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.215
Variable
F Q2
N
47
Mean
2.957
StDev
1.215
SE Mean
0.177
95% CI
(2.610, 3.305)
ACCEPT NULL… F Q2 = 3
One-Sample Z: F Q3
Test of mu = 3 vs not = 3
The assumed standard deviation = 1.368
Variable
F Q3
N
47
Mean
2.723
ACCEPT NULL… F Q3 = 3
StDev
1.363
SE Mean
0.200
95% CI
(2.332, 3.115)