What is the volume of a right circular cylinder in terms of Pi if its height measure 6 inches and the radius of its base is 2 in
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Answer:
Step-by-step explanation:
From the given information:
Let's first compute the null and alternative hypothesis
Null hypothesis:
Alternative hypothesis:
The number of samples is half in a group of 60
i.e
the sample mean for sample 1 = 5.7
the standard deviation for sample 1 = 3.1
the sample mean for sample 2 = 3.9
the standard deviation for sample 2 = 2.7
degree of freedom for this test can be computed by using the formula:
df = 114.68
The test statistics can be computed as follows:
t = 1.07
Using the level of significance of 0.1, the P-value for the test statistics at the df of 114.68 is:
P-value = 0.143
Decision rule: To reject the null hypothesis if the level of significance is greater than the p-value.
Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance at 0.1.
Thus, it appears that the true average weight loss for the vegan diet does not exceeds that for the control diet by more than 1 kg.
Let us first make the sample space for the event A. The Sample Space will be:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5)
(5,1) (5,2) (5,3) (5,4)
(6,1) (6,2) (6,3)
As can be clearly seen the Sample Space for the event A has 30 elements in it.
Now, it is given in the question that the event A has already occurred and we need to find the probability of the event B occurring <u><em>given that the event A has already occurred.</em></u>
Now, as we can see, from the sample space, only 11 events out of the 30 are the events of interest to us. This is shown in bold below:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5)
(5,1) (5,2) (5,3) (5,4)
(6,1) (6,2) (6,3)
Thus, the probability that the event B occurs given that the event A has already occurred is:
In percentage the required probability is 36.7% approximately.