James buys 7 baseballs and 1 bat.
2 answers:
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Answer:
b) B and D and c) A and C
Step-by-step explanation:
The hypotheses would be:
(Right tailed test at 5% level)
Sample proportions are
Sample A B C D
Success 31 34 27 38
Proportion p 0.775 0.85 0.675 0.95
Std error
(sqrtpq/n) 0.066 0.056 0.074 0.034
p diff
p-0.75 0.025 0.10 - 0.075 0.20
Z stat
p diff/SE 0.0757 1.77 1.01 5.80
p value 0.469 0.038 0.156 0.000001
we find that p value is more smaller than alpha, the more accurate the alternate hypothesis.
b) Only B and D provide against the null. Because p <0.05
c) A and C provide no evidence for the alternative because p >0.05
Answer:
a)
b)
c)
Step-by-step explanation:
Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.
To find : The following probabilities by summing the probabilities of the appropriate sample points ?
Solution :
The sample space is
S={HHH,HHT,HTT,HTH,TTT,TTH,THH,THT}
n(S)=8
A: At least one head is observed
i.e. A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}
n(A)=7
B: At least two heads are observed
i.e. B={HHH,HTT,TTH,THT}
n(B)=4
C: The number of heads observed is odd.
i.e. C={HHH,HTT,THT,TTH}
n(c)=4
a) Probability of A, P(A)
b) P(A or B)
Using formula,
(c) P((not A) or B or (not C))
A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}
not A = {TTT} = 1
B={HHH,HTT,TTH,THT}
C={HHH,HTT,THT,TTH}
not C = {HHT,HTH,THH,TTT} = 4
So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5