1
Wheat Yield per acre for 32 test acres as a percent of National Average
Wheat Yield O-Yield
C-Yield
P-Yield
NP-Yield
104
104
104
94
94
94
85
85
85
113
113
113
98
98
98
105
105
105
95
95
95
145
145
145
111
111
111
126
126
126
101
101
101
108
108
108
141
141
141
119
119
119
119
119
119
106
106
106
94
94
94
105
105
105
100
100
100
86
86
86
109
109
109
74
74
74
121
121
121
79
79
79
114
114
114
73
73
73
88
88
88
114
114
114
111
111
111
94
94
94
89
89
89
131
131
131
Fertilizer
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Organic
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Pesticides
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
No
2
Wheat Yield
O-Yield
C-Yield
P-Yield
NP-Yield
32
16
16
16
16
0.30
0.78
0.13
0.97
-0.27
0.03
0.34
-0.81
1.99
0.16
No
No
No
Yes
No
104.7500
110.6250
98.8750
100.4375
109.0625
17.5094
16.3702
17.0875
17.1619
17.3031
3.0953
4.0925
4.2719
4.2905
4.3258
5%
5%
5%
5%
5%
100
100
100
100
100
1.5346
2.5962
-0.2634
0.1020
2.0950
2.0395
2.1314
2.1314
#N/A
2.1314
Don’t Reject
Don’t Reject
Don’t Reject
Ho: mu might Reject H0: mu Ho: mu might
Ho: mu might
be 100
isn't 100
be 100
#N/A
be 100
Decision
Does Type of Fertilizer
Does Type of Pest Control
Matter?
Matter?
11.7500
8.6250
Observed Difference
279.9833
296.9625
Pooled Variance
16.7327
17.2326
Pooled Standard Deviation
5.9159
6.0926
Standard Error
1.9862
1.4156
calculated t statistic
Critcal t (2 sided)
2.0423
#N/A
n
Skewness
Kurtosis
Reject notmal popul?
xbar
s
standard error
Significance
mu-naught
Calculated t or z statistic
Critical t or z, 2 sided
Decision
Don't Reject Equal Means
#N/A
3
A
36
37
38
39
40
41
42
43
44
45
46
47
n
Skewness
Kurtosis
Reject notmal popul?
xbar
s
standard error
Significance
mu-naught
Calculated t or z statistic
Critical t or z, 2 sided
48 Decision
49
50
51
52
53
54
55
Observed Difference
Pooled Variance
Pooled Standard Deviation
Standard Error
calculated t statistic
Critcal t (2 sided)
56 Decision
B
=B2
=COUNT(B3:B34)
=SKEW(B3:B34)
=KURT(B3:B34)
=IF(MAX(ABS(B38),ABS(B39))>1,"Yes","No")
=AVERAGE(B3:B34)
=STDEV(B3:B34)
=B42/SQRT(B37)
0.05
100
=(B41-B45)/B43
=IF(B40="Yes",-NORMINV(B44/2,0,1),TINV(B44,B37-1))
=IF(ABS(B46)>B47,"Reject H0: mu isn't 100","Don’t Reject Ho: mu might be 100")
4
36
37
38
39
40
41
42
43
44
45
46
47
C
=C2
=COUNT(C3:C34)
=SKEW(C3:C34)
=KURT(C3:C34)
=IF(MAX(ABS(C38),ABS(C39))>1,"Yes","No")
=AVERAGE(C3:C34)
=STDEV(C3:C34)
=C42/SQRT(C37)
=B44
100
=(C41-C45)/C43
=IF(C40="Yes",NA(),TINV(C44,C37-1))
D
=D2
=COUNT(D3:D34)
=SKEW(D3:D34)
=KURT(D3:D34)
=IF(MAX(ABS(D38),ABS(D39))>1,"Yes","No")
=AVERAGE(D3:D34)
=STDEV(D3:D34)
=D42/SQRT(D37)
=C44
100
=(D41-D45)/D43
=IF(D40="Yes",NA(),TINV(D44,D37-1))
48 =IF(ABS(C46)>C47,"Reject H0: mu isn't 100","Don’t Reject Ho: mu might be 100") =IF(ABS(D46)>D47,"Reject H0: mu isn't 100","Don’t Reject Ho: mu m
49
50
51
52
53
54
55
Does Type of Fertilizer Matter?
=C41-D41
=(C42^2*(C37-1)+D42^2*(D37-1))/(C37+D37-2)
=SQRT(C51)
=SQRT(C51/C37+C51/D37)
=C50/C53
=IF(C40="Yes",NA(),IF(D40="Yes",NA(), TINV(D44,C37+D37-2)))
56 =IF(ABS(C54)>C55,"Reject equal means","Don't Reject Equal Means")
5
36
37
38
39
40
41
42
43
44
45
46
47
E
=E2
=COUNT(E2:E34)
=SKEW(E2:E34)
=KURT(E2:E34)
=IF(MAX(ABS(E38),ABS(E39))>1,"Yes","No")
=AVERAGE(E2:E34)
=STDEV(E2:E34)
=E42/SQRT(E37)
=D44
100
=(E41-E45)/E43
=IF(E40="Yes",NA(),TINV(E44,E37-1))
F
=F2
=COUNT(F2:F34)
=SKEW(F2:F34)
=KURT(F2:F34)
=IF(MAX(ABS(F38),ABS(F39))>1,"Yes","No")
=AVERAGE(F2:F34)
=STDEV(F2:F34)
=F42/SQRT(F37)
=E44
100
=(F41-F45)/F43
=IF(F40="Yes",NA(),TINV(F44,F37-1))
48 =IF(ABS(E46)>E47,"Reject H0: mu isn't 100","Don’t Reject Ho: mu might be 100") =IF(ABS(F46)>F47,"Reject H0: mu isn't 100","Don’t Reject Ho: mu mig
49
50
51
52
53
54
55
Does Type of Pest Control Matter?
=F41-E41
=(E42^2*(E37-1)+F42^2*(F37-1))/(E37+F37-2)
=SQRT(E51)
=SQRT(E51/E37+E51/F37)
=E50/E53
=IF(E40="Yes",NA(),IF(F40="Yes",NA(), TINV(F44,E37+F37-2)))
56 =IF(ABS(E54)>E55,"Reject Equal Means","Don't Reject Equal Means")