e as the central theoremn states that if there is a large number of independent and identiacally distributed random variable, then the distribution of their sum tend to be normally distributed as the number of these variables increase indefinitely therefore the distribution does not have to normally distributed.
(c) A sample of 100 taken , probability will be between 198 and 220
Z = mean – X/ standard deviation
198=&gt. 198 – 211/ 9 = -1.444
Z = 0.07493
220 =&gt. 220 – 211/ 9 = 1
Z= 0.15865
Area between the two Z points
Prob. = 1- (0.07493+0.15865)
Prob. = 0.76642
Unit test three
1. 99 %
Mean = 2
Standard deviation = 10
SD= SD/ (N)1/2
2. 160 infants
Mean = 5.98
SD= 3.5
95% confidence level
= (5.98 -( 3.5 X 1.6) X (5.98 +( 3.5 X 1.6) = 95%
= 0.38 X 11.58 = 95%
3.
(a) Paralyzed
(48.0 – (8.1 X 1.04) X (48.0 + (8.1 X 1.04) = 98%
(39.576) X (56.424) = 98%
None polarized
(56.7 – (8.1 X 1.04 ) X (56.7 + (8.1 X1.04 ) = 98%
(48.276) X (65.124) = 98%
(b) Conclusion
The two confidence intervals are different. therefore there is a difference in the two means.
4.
(a) Type I: when we reject the null hypothesis when it should be accepted.
(b) Type II: when we do not reject the null hypothesis when it should be rejected.
(c) Z= 2.33
P value is 0.4901
5.
(a) null hypothesis
H0 : U &lt. 15
Ha : U = 15
(b) t= 0.6107
P value = 0.7269
T critical is greater therefore we accept the null hypothesis
6.
(a)
H0: U &lt. 22000
Ha: U =22000
(b)
(c) t calculated = 21819/ 1295 = 16.84
T critical = 1.29
T critical is less than T calculated therefore we reject the null hypothesis
(d) Because we have rejected the null hypothesis it is still true to state that the tires last 22000 miles…
T critical is greater than T calculated so we accept the null hypothesis that the change as a result of training is equal to zero, therefore the training makes some positive change towards those who are mentally retarded.

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