MA205- Elementary Statistics Essay Example | Topics and Well Written Essays - 2250 words

MA205- Elementary Statistics - Essay Example 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=> 198 - 211/ 9 = -1.444 Z = 0.07493 220 => 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 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 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.