Statistics Problems and Solutions
[Name of the Institute]
Question no. 11
PART 1.1
PART 2.1
PART 3.2
Question no. 23
PART 1.3
PART 2.3
PART 3.5
Question no. 37
t-test Paired two sample for means:8
Level of Significance:8
t-Test: Paired Two Sample for Means9
Decision:9
Question no. 410
t-test two sample assuming unequal variances:10
Level of Significance:10
t-Test: Two-Sample Assuming Unequal Variances11
Decision:11
References13
Question no. 1
PART 1.
Here the probability of success = P = 0.95
N = 3
Q = 1-P = 0.05
X = 0,1,2,3
The formula for Binomial probability is
P(X) =
For the probability that three bypass surgeries are successful
P(X) = + + +
P(X) = 0.0012 + 0.00712 + 0.13537 + 0.85737
P(X=3) = 1
The probability that all three bypass surgeries will be successful is almost 1.
PART 2.
Here the probability of success = P = 0.95
N = 3
Q = 1-P = 0.05
X = 0
The formula for Binomial probability is
P(X) =
For the probability that three bypass surgeries are successful
P(X) =
P(X) = 0
P(X=0) = 0.0012
The probability that none of the bypass surgeries will be successful is 0.0012.
PART 3.
Here the probability of success = P = 0.95
N = 3
Q = 1-P = 0.05
X = 0,1
The formula for Binomial probability is
P(X) =
For the probability that three bypass surgeries are successful
P(X) = +
P(X) = 0 + 0.007125
P(0
The probability that atleast one of the bypass surgeries will be successful is 0.0083.
Question no. 2
n(S) = total no. of donor or sample space = 409
n(O)= total no. of donor of blood type O=184
n(A)= total no. of donor of blood type A=164
n(B)= total no. of donor of blood type B=45
n(AB)= total no. of donor of blood type AB=16
PART 1.
Probability that the donor has type O blood
P(O)= Probability that the donor has type O blood
P (O) = = = 0.44
The probability that a donor has type O blood is calculated as 0.44. This means that there is a 44% chance that out of the total a type O blood donor is selected.
PART 2.
Probability that the donor has type O or type A blood
P(O)= Probability that the donor has type O blood
P(A) = Probability that the donor has type A blood
The Probability that event A or event B occurs is calculated by the formula
P (A ? B) = P (A) + P (B) - P (A n B))
Where,
P(A n B) = P( A )P( B | A )
So, Here,
P (O ? A) = P (O) + P (A) - P (O n A))
Where,
P (O n A) = P (O) P (A | O)
Probability that donor has blood type O
P (O) = = = 0.44
Probability that donor has blood type A
P (A) = = = 0.40
Probability of obtaining a donor that has blood type O times the probability that the donor has blood type A, given that donor with blood type O are obtained.
P (O n A) = P (O) P (A | O)
= *
= 0.4498 * 0.6413
= 0.28933
Now for the Probability that the donor has type O or type A blood
P (O ? A) = P (O) + P (A) - P (O n A))
= ...