1)
2)
95% of confidence intervals I could do with 40 trials would capture the true average
95% of the time this method is used, it will correctly capture the population average
3)
Reject if xbar is above 2.33+2.33*20/sqrt(36) so reject if xbar is above 127.8
The z-score for that is z=(127.8-125)/(20/sqrt(20))=0.83
Power is 0.2033
4) H0: µ ≥ 3.93
Ha: µ < 3.93
α=0.05
t145=(3.85-3.93)/.85/sqrt(146)
0.10 < p-value < 0.15
Fail to Reject
No, this class is not significantly less work than other classes in the department
5) H0: Social skills is not related to intelligence
Ha: Social skills are related to higher intelligence
α=0.05
z-test: (56/125-73/135)/sqrt{ 129/260*(1-129/260)/125 + 129/260*(1-129/260)/135 } = -1.49
Chisq:
Obs: 56, 69, 73, 62
Exp: 62.02, 62.98, 66.98, 68.02
Chi: 0.584, 0.575, 0.541, 0.533
p-value = 0.1362
0.10 < p-value < 0.15
Fail to reject
We cannot show poor social skill is related to intelligence
6) (263.14-277.24)+-2.626*7.2/sqrt(600) = (-14.87, 13.33)
7)
There are multiple answers, but here are the main two possibilities. The main thing to notice is how
interconnected everything is. You can’t change the MSE without needing to change either SSE or DFE
(and the standard deviation too)
Regression Statistics
Multiple R
0.698729
R Square
0.488222
Standard Error
77.28074
Observations
20
ANOVA
Df
Regression
Residual
Total
SS
MS
1 102553.6 102553.6
18 107501.6 5972.313
19 210055.2
F
17.1715
P-value
0.00061
Coefficients Std Error
t Stat
P-value
Intercept
-2.48371 32.63094 -0.07612 0.940167
length
5.615491 1.355138 4.143851 0.00061
Regression Statistics
Multiple R
0.698729
R Square
0.488222
Standard Error
77.28074
Observations
20
ANOVA
Df
Regression
Residual
Total
SS
MS
1 102553.6 102553.6
18 107501.6 5972.313
19 210055.2
F
17.1715
Coefficients Std Error
t Stat
P-value
Intercept
-2.48371 32.63094 -0.07612 0.940167
length
5.615491 1.355138 4.143851 0.00061
8)
Group
DF
1
SS
82.559
MS
82.559
F
5.934
P-value
0.00061
Error
Total
26
27
361.7354
444.29
13.9129
9) 256/400+-1.75*sqrt{ 256/400*(1-256/400)/400} = (0.598, 0.682)
10)
A z-test if I assume normality and assume the standard deviation is the true sigma
A t-test if I assume normality
11)
OBS
Mechanical
Civil
Electrical
Chemical
City
26
44
63
45
Suburb
36
33
45
59
EXP
Mechanical
Civil
Electrical
Chemical
City
31.44
39.05
54.8
52.8
Suburb
30.6
38.0
53.2
51.2
X2
Mechanical
Civil
Electrical
Chemical
City
0.94
0.63
1.24
1.14
Suburb
0.97
0.65
1.27
1.17
12) None of the above
13) .03/2=1.645*sqrt(.01*(1-0.01)/n)
Then n=119.06
Need 120 engineers
14) 0.08<p-value<0.10
15) You can’t get negative values, but the normal sticks out past the 0, which means there is always a
risk of getting negative (unrealistic) answers
If the confidence level is too high then the results may not be realistic, and 99% must be too high
The rule of n > 30 doesn’t mean it’s exactly normal, and this shows a time when that rule fails
16) (4.3-3.4)+-2.021*sqrt(1.7^2/50+0.9^2/70) = (0.367, 1.432)
17) Students should be able to explain where they are seeing clumping – Not random
There is a fan shape at the right end – non constant variance
The clump on the top left could be part of a fan shape with clumping – or students may say that is a
clump around an outlier calling normality into question. In that case they may describe a swerve
pattern from bottom left to mid right which violates linearity.
18) The biggest winners were telling the matched pairs from the pooled tests, ANOVA, and the
definition of confidence.